Alright, so read through the class and have a list of things that jumped out to me right away.
1. The language was a very unclear in places as to what you were trying to say and you broke writing convention to talk to the audience directly several times. This is generally considered a no-no. Try to keep your language consistent and try to model it after existing classes, it makes for a much easier read.
1b. In a related vein, you should try to keep out as much "fluff" from a class write up as possible, focusing more on the "crunch." There were several cases, such as in the case of Weapon Growth where you went into unnecessary detail on HOW things were done instead of simply telling us WHAT happened; there were full sentences that could be chopped out of the description.
2. There are some editing issues with the document, such as the Bonus Feat section stating that the Meister effectively receives a feat every level when levels 6, 10, 14 and 18 don't actually hand out feats (and 2nd level only hands out a bonus feat through a different ability), the fact that one ability is called Fast Travel in the table but Fleet Feet in the ability description and that you repeat the last sentence in the Soul Link section. Good editing is arguably even more important that clear language, just look at how much of the errata to the Advanced Class Guide was fixing editing mistakes because people were appalled by the quality of the editing in the first print.
3. Questions on First Bond:
3.1. Outsiders normally do not have a separate body and soul, they are a unified entity. What happens when they are turned into their weapon form?
3.2. While it is stated that mind altering effects cannot make the weapon break their bond with the Meister, nothing is stated about the opposite. What happens when a Meister is dominated and told to break their bond with their weapon?
3.3. Can you use this ability to gain any humanoid shaped creature as your bond? Nothing in the ability says that you have to bond with the cohort you get from Soul Link, so what's stopping you from bonding with a Solar Angel at 3rd level?
4. Soul Link was fine as is, but perhaps some kind of class guideline on the cohort as it gains hit dice would be worthwhile. Weapons from Soul Eater generally weren't studying to be clerics or wizards after all.
5. Soul Eating needs to be reworked since it's pretty abusable. If you decided to go on a toad killing spree at 19th level, you could take out over twenty thousand toads before you leveled up, netting you over twenty thousand soul points, whereas fighting level appropriate challenges would net you just under a hundred (14 CR 20 enemies would equal 84 soul points). Perhaps limiting collecting soul points to creatures whose CR is no lower than your class level-4 would be a good benchmark (it's the limit for recovering grit, panache and other like pool points for other classes) and would get rid of the possibility of gaining HUNDREDS of stat points per level for your weapon, although getting 1-2 stat points per level would still be pretty easy to do and is still too strong.
6. Soul Resonance is fine as is, but perhaps changing it to 3 + Con modifier times per day would be better. Most abilities that run off of an ability score either are usable 3 + ability mod times per day or state a minimum value in case of a negative ability score.
7. Fleet Feet needs its name clarified, but the ability itself is fine, if a little underwhelming.
8. Unburdened shouldn't have to be a thing, the custom weapon weight formula you have makes for weapons that are too heavy for dexterity builds so should be revised to accommodate for low strength scores (or alternatively, bonded weapons duplicate all stats of whatever weapon they physically emulate)
9. Weapon Growth requires too many souls, it costs twenty thousand to get up to a full +10. There is no way you can expect someone to accurately keep track of that many when they're only gaining souls 1-7 at a time. It would be better to just have the weapon gain an enhancement bonus every X levels.
10. Greater Bond is ambiguous on whether you get to add 3x Str (1.5 from Improved Bond x2) or just 2x Str
11. Considering how late of a level you get Weapon Jumping, you should be able to teleport it from much farther away. Bladebound Magi can teleport their Black Blades from a mile away at 9th level.
12. The weapon form stats are awkward and extremely easy to break. A bond with 30 Dexterity, Intelligence and Charisma (not hard to do at all) would make a 6d6 15-20/x5 weapon. That's far too powerful. Damage dice progression can probably be left as is since you don't have a good in-class way of boosting your to-hit (outside of spending soul points on your bond's Wisdom stat) and having a high critical hit range is powerful but not broken, but the critical multiplier will almost guaranteed be a x3 or greater, which combined with the other two aspects makes for far too strong of a weapon. Critical Multiplier = 1+1/4 Dex mod; Max x4, makes for a slower but still usable formula. Honestly though, I think that the weapon stats should be same as whatever weapon the bond emulates, with maybe also allowing damage dice progression at half the rate that you currently have.
13. I didn't have any mechanical issues with the armor (although you can make an incredibly powerful shield with the current formulas) but it is still a really awkward system for setting up the armor's stats. Again, choosing what armor to emulate and then enhancing it at a slower progression feels like a more appropriate way to go.
14. The class doesn't really bring anything unique to the table outside of either having an overpowered weapon or an over-statted cohort (who is honestly more useful when not in their weapon form). I'd give the class a bit more of a niche by changing Soul Eating to an ability where you can get +X to either to-hit and damage (if bond is a weapon) or to AC (if bond is armor) for a certain length of time after you consume the soul of a fallen foe (the to-hit should probably be for 1 minute or min/level and the AC bonus should probably be for 1 hour or 10 min/level) instead of stockpiling up on souls. X would be the number of soul points the soul would be worth based on your current soul point formula. You could still stockpile souls, but you wouldn't be able to use them for static buffs, instead you could use them to perform special combat abilities that the Meister can only use while their bond is in their alternative form. A customizable list of signature abilities if you will. More potent abilities would cost more soul points to activate. Tome of Battle could be a good source of inspiration for this (as of course Soul Eater itself).
Path of War should help expand on things while keeping a similar flavor and power level. Mythic Adventures has some nice flavorful abilities as well, but the power of them is all over the place.
EDIT: By the way, the edits look nice. Once you figure out how you want to add in some flair to the class I think the class could turn out quite nice.
I had seen another soul eater homebrew on here and I was trying to help them with some of their ideas and putting them into a class. Another way to look at this class is to think of it as a combination of a summoner and a fighter. The summoner aspect being that you have this cohort of sorts, (similar to how a summoner would have an eidolon), and then give the player some aspects of a fighter, like maybe how a fighter gains a bonus feat on their even levels.
Take out how the normal summoner gets spells but still give them a unique evolution pool where that pool is your soul points from earlier, but not at the sheer scale that you were talking about instead the player as they level gain access to more "soul points" which they can use to give unique bonuses to their cohort, weapon, thing.
Things such as:
Dual Wielding (1 SP)
A Meister weapon with this Soul point splits into two weapons of either two light one handed melee weapons, or one light handed melee weapon and a one handed melee weapon. These weapons are of a size category equal to your size or one size category smaller. This Weapon evolution cannot be chosen with the Double Weapon evolution or Two-Handed Weapon evolution. If the weapon has an enhancement bonus, the bonus must be split evenly between the two weapons.
Again, this is an idea, I am not completely knowledgeable on how the math works on for what balances where but this was an idea of how to go about executing the cohort weapon strengthening mechanic.