The engine starts normally because it requires more gas to start the engine and the mixture must be richer which is why you have to choke it.
So starting easily with a stuck float seems very normal.
What is happening is that the gasoline is overflowing the bowl just like the toilet would keep running if that valve stuck.
So the gas, is leaking into the OIL and making it thinner.
This thinner oil will seep past the rings, valve guides, and piston.
Then it burns up in the cylinder and smokes (it may drip out of the muffler and out of the breather).
If you continue to run the engine you will destroy it because the thinned gasoline will not do much of any lubricating at all. EVERY Part that touches oil will get damaged.
You Need to clean and overhaul the carburetor.
Pay particular attention to the needle and seat to make sure they are replaced and the area where the seat is very clean.
Most likely you have a fuel delivery or fuel quality problem.
As engines sit or get older, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems.
Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
Today's gasolines contain MTBE and alcohol. (Ethanol) They turn to "Junk and garbage" very quickly. Alcohol absorbs water. And they call it "Oxygenated fuels! It is the oxygen (and the water) that breaks down the organic compounds in the fuel and turns the gas to "Garbage" (Gum and varnish) The fuels we had just a few years ago had no alcohol in it and would store for longer periods of time before going stale.
Fuel stabilizers do almost nothing to prevent the fuel from going bad with the changes in today's fuels. The whole point of a fuel stabilizer is to form an oily film on the surface of stored gasoline whether in the tank or in a gas can. The idea was to keep oxygen away from the gasoline to prevent breakdown. Since the fuel is already oxygenated, the fuel stabilizer concept is null and void. These fuels start to degrade immediately upon the addition of the ethanol.
Do not buy gas from the "Discount" Stations. The discount stations get a reduced price on gas because they may be buying fuel that is nearly 30 days old already. You may be getting fuel that's nearly stale right from the pump when buying from a discount station. Purchase your fuel from the well-known stations such as Shell, BP, Sonoco, Phillips 66 etc.
More than 70% of all of our repairs in our small engine repair business are due to these same issues. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carburetor.
The carburetor will need to be cleaned and overhauled as well as the rest of the fuel system.
In an Emergency such as a blizzard where you cannot get out to buy a carburetor kit until the plows come through, or during an emergency power outage and you need a generator running even if it runs poorly, you might try the following if your carburetor is the type that has a bowl. Sometimes this procedure works:
While the carburetor is still mounted to the engine:
You may be able to finish the job at hand then clean and overhaul the carburetor correctly when you have more time and a new carburetor overhaul kit.
If you don't feel comfortable with these kinds of repairs, or if the carburetor still doesn't work correctly after your attempt, I would suggest sending it to a profession repair shop with a reputation for having friendly, knowledgeable, experienced service technicians. It would be best to take it to someone who has an "Ultra-sonic" cleaning machine. This machine uses a very mild carburetor cleaner in concert with ultrasonic vibrations to get the very small passageways clean. This method is very effective even when traditional methods fail.
Please feel free to ask follow-up questions so that we can always arrive at the correct solution. We want you to be 100% satisfied.