ive seen many adaptors to put briggs carbs on tecumseh engines, and vise versa. but the big question to me is why would you want to? tecumseh engines (stock) seem to have many problems with their carbs. if you are wishing to put a bigger carb in your little 3 hp engine, why go to a different manufacturer?
if the 6 or 7 hp carb will work on t he 3 hp, without flooding it like i would think it would, you could just as easily to adapt a 5, 6, or 7 hp briggs carb onto it.
if you build up the 3hp with a good cam, lighter flywheel, stiffer valve springs, lighter piston, billet rod, offset flywheel key and possibly a bore over then i could see a reason to use something like a 8hp carb, maybe, due to the extremely high rpm's you could/would turn.
if you really just want to but a slightly larger carb on the 3 hp, to see if it helps with power any, get a 5hp carb, and make an adapter.
-Phil