I have a Troy-Bilt rototiller that I put back into service recently (piston was rusted in place; exhaust valve was rusted shut; etc.), but I still have one major issue with it, and that is that the float carburetor constantly leaks gas out of the air intake (when it is on or off). The gas tank is above the carburetor, so it makes sense that the gas could get down there by gravity, but evidently the carburetor shouldn't leak gas all the same. What's likely going on here?
More than likely the float is saturated or non-existent, allowing the bowl to be over filled constantly (not stopping the flow of fuel into the carb). It could also be the needle valve not seating correctly allowing the same thing to happen. You can try replacing the float/needle valve (there are generally kits for this), but personally, every time I've tried to rebuild a small engine carb, it doesn't end well.
Realistically, just replace the carburetor. Most of the carbs for these small engines are relatively cheap and plentiful. Unless you truly have a wish to get it fixed on your own, the time versus expense strategy leaves this well in the replacement camp.
Either the floats don't float, or the needle doesn't seal.
In a working system: As fluid fills the bowl, the float rises, and a needle plugs the hole through which gas was entering the bowl. Then, as fluid from the bowl is used, the floats sink a little, the plug falls to a lower level and stops plugging, more gas enters, the float level raises, and the cycle continues until gas is no longer being used.
If the needle plug never plugs (either from not being floated up there, or from being too dry/coarse of rubber), then you have an open path from gas tank to carb that never closes, and so overflows into the carb body, and then backpours into either the engine intake or the airbox, depending on the orientation of the carbs.
The floats may need to be replaced (they may have a hole, or be misshapen, or have a damaged axis), or the needle may need to be replaced (it can dry out, become misshapen, come off, etc.), or the seat may need to be replaced (it could have been nicked or cracked, etc.).
Carb rebuilds are very doable, but it's delicate precision work that requires some sensitivity and intuition built up by practice and experience--not complicated, just sensitive.
Most Carburetors have a Needle and Seat
Your float needle is not sealing against the seat properly allowing the gravity fed fuel to continue to flow threw your main jet as the fuel levels rise in your carburetor.
Some of these small carburetors have a diaphragm along with the float so you may also have to replace the rubber diaphragm where you would see a float system of fuel regulation. It would depend on the model.
Replace your needle and seat (and rubber diaphragm if necessary).