I have to differ greatly with Dave...
I am pretty sure that his first intuition was correct, The carburetor is the issue, or more specifically the Accelerator pump is not working properly in the carburetor. The accelerator pump works by actually "Squirting" raw fuel into the throat of the carburetor when the throttle is advanced. The reason for this is to give the engine a shot of fuel to catch up in RPM and the Carburetor time to catch up with the engine. If you advance the throttle supper slow you don't need this extra fuel, only when you advance the throttle quickly or even normally do you need the "Shot".
Take a look down the throat of the carb and have a friend advance the throttle. You should see Two steams of fuel "Squirting" Into the throat as the throttle is advanced. Spitting fuel from the accelerator pump system doesn't count, and is bad....
Marine Mechanic
21 Years Experience as Mechanic, 18 Yrs Boat Yard Owner/Mechanic, Factory Certified