Doesn’t stability do that already? It affects ship quality and fleet size of the colony.
Population does not affect ship quality or fleet size, and colony level would only take certain effects away from pop. So no, stability and colony level are unrelated.
Related idea by mendonca where each industry has its own size
One thing that's jank about the current implementation, which this and that suggestion would address, is how upsizing a colony makes it more productive without any actual infrastructure spending. An industry on a size 3 planet has the exact same construction cost as one on a size 6 planet, but the second is way better (this has a bunch of implications for Nex and vanilla gameplay).
I think upgrade systems like that are bland and uninspiring, though I can understand why many space games do it that way. It is much easier to come up with believable upgrade names and stuff for historical games like Civilization. Contrast GalCiv2's Xeno Farm Construction 3 tech with Civ4's Biology tech - both increase food production from farms, but Biology is more interesting lore-wise and has additional benefits inspired by its lore.
In that vein, increasing your colony level could be done in a concrete way: upgrading your spaceport. Something like Outpost -> Makeshift Port -> Spaceport -> Megaport. A few tricks could add a lot of nuance to that base upgrade path. For example, Spaceport could make your colony immune to instant wipeouts from sat-bombing (as pop 4 currently does, I think?), but require a structure called Cerametal Plant to be built first. If Cerametal Plant required a blueprint to be built, that would create a natural gate between the player as a Space Cossack and the player as a faction leader.
Another trick could be splitting colony level progression between the base level provided by the spaceport and bonus levels provided by structures like Cerametal Plant. For example:
Outpost = level 1
Outpost + Cerametal Plant = 2
Makeshift Port = 2
Makeshift Port + Cerametal Plant = 3
Spaceport (absorbing the Cerametal Plant) = 4