Why does my boat engine hesitate when opening throttle fast from idle?

The gas has to catch up with the sudden influx of air. This is probably a normal condition depending on what type of motor you have and how much it hesitates.

If it hesitates for what seems like too long, it could be a number of things. It could be from jets in the carburetor being slightly gummed up. If it has a points system it could be due to the points being out of adjustment. A tune up wouldn't hurt to start with.