How old is your motor, and when did the problem start? Most motors are suppost to blow smoke when you first start them on choke. If your seeing puddles of gas in your airbox then I would see if your valves are adjusted properly and your carb is clean.

Motor is 3 years old. Problem just started last week. The white smoke it blows is thick and heavy, even will spew a little unburned gas out the muffler. It's not choked heavily (nor has it ever needed it) to start. Once the smoke clears it runs clean and smooth. I suspect the carb, but wanted a few sanity checks before I go in. It almost seems to let gas collect while it sits unused.

Post your engine's model numbers so we know what you have.
Brigg's newer carbs are a bit fussy, and have a bad habit
of leaking past the float/needle while sitting, so I would
suggest installing an inline fuel shutoff. Over time,
gas will foul your oil and possibly damage your engine.
Fish

Model 21A907 Type 0120-E1

There already is a inline shutoff, I'm going to give the carb a good cleaning and cut the fuel after use to see if it helps. I've seen well worn carbs leak past the needle while unused, wouldn't expect that kind of behavior with this one yet. I've also noticed that the outside of the carb itself has a caked buildup and is a little moist as if there were seepage.