Have a tach? Idle speed in the water, boat moving in F gear should be around 675 set by your throttle linkage knurled idle set screw on one of the arms (the arm) connected to remote throttle linkage inside the engine. Fast enough to take going into gear but slow enough to engage with out a "clunking" of the drive train. If you have that and there is nothing actually wrong with your engine your idle mixture screw is used to prevent what you are experiencing. It is only opened enough for you to hammer down on the throttle from the above condition and the engine take the throttle, put the boat on plane, and not hesitate.
If you do/try to do that and it fails, you need to start cleaning up your fuel system starting with cleaning your carbs and installing new kits, a new fuel pump kit wouldn't hurt as the diaphragm gets stiff with age and doesn't pump like new, maybe a new fuel filter (cut the old one open and if black dots or crystalline tan particles do what I suggest next. Swab out a couple of your internal fuel lines and if little black flakes inside, replace the lines; a new bulb and fuel line to the tank probably wouldn't Hurt..........all just little things that should be done over the years that you may not have known needed to be done.