Because I wanted to adapt items from other games into Starfinder, I decided to make a spreadsheet on Google Drive that would have the average damage amount for most, if not all, weapons in the game for a specific level in order to give me some sort of formula or framework for creating new weapons, and to figure out how much adding crit effects or special qualities should affect damage. Eventually, I wanted to do the same with price.
What I've done so far has helped me, but I'm a layman when it comes to statistics, and this is... a lot for one person to do, I've realized. I'm sure there are plenty of other GMs out there that would benefit from this type of document and have some time to spare to help it grow!
One of the more interesting things I've learned while doing this is that there's a "dead zone" between level 2 and 7 where there are very, very few weapons.
This seems to be because the rate at which damage slowly ramps up would required something between 1d4 and 1d6, which can't be done, so any items that DO fall inside here either have more stacked advantages (rare damage type, multiple special properties, etc.) to push them up a level or two, or a drawback to lower them down.
I ran across this site https://www.sfrpgtools.com/weapon-generator
Not sure who made it but it seems to do the job very well and could give you some insight. To your point about the dead zone, I have a hunch it is tied to how NPCs / Monsters are created. I was playing with the NPC creation rules in Alien Archive recently as I needed to re-balance the campaign my party is currently on due to group size increasing recently and noticed that the damage of weapons currently is tied very closely to expected damage output of NPCs arrays at various lvls. My hunch, and I hope im wrong, is that they purposely gapped weapon damage so that PC damage would coincide with NPC damage and control scaling issues between the way NPCs and PCs are built and interact. If im right then that gives me less hope these gaps will be addressed by the gear book that is coming out but there is an a appearance of a pretty strong correlation between them once you really look into the arrays and the weapon tables.