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First you would have to explain how an improvised weapon would ever be other than appropriately sized for the wielder. (I'm not saying you can't; I'm saying that without more context/explanation I don't understand what you expect those words to mean. Very much a "colorless green ideas sleep furiously" situation.)
You take the size of the object and convert it to a weapon. A light = 2 sizes smaller than the wielder. Medium = 1 smaller. 2H = same size.
So if you take a tree you'd convert it thusly, and since it's large it doesn't fit any of these so you say it's meant for large as a large 2H weapon.
Not saying this is rules, but it's an explanation of how an improvised weapon might be different than your sized.
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My understanding of the improvised weapon rules is that the reference weapon depends on *how you wield it* not on *what it is*.
So if you are wielding it like a one-handed club, it does damage as a one-handed club of your size, regardless of how large a piece of wood it is.
I may of course be mistaken. Wouldn't be the first time.
So how would you wield a tree larger than you? Can you wield it as a one-handed club cause you say you do? Or can you only say you're wielding it in a manner that is appropriate if you converted it to a weapon?
If it's the first then you just say you're wielding it as a large two handed weapon. "yes my toothpick is being wielded as a large two handed improvised weapon, shut up, I get better bonuses this way"
If it's the second than a large tree and a toothpick are to large or small to be used by a medium person as an improvised weapon.
*note, I'm not actually looking at the rules for any of this. I'm just throwing out ideas from what I remember