First check your spark arrestor screen. If highly loaded up with crud, it can do this.
Is this a fuel injected or carbureted engine?
If it is carbureted, then a carburetor rebuild is probably overdue. Here is one simple test you can do to see if the engine is starving for fuel at the higher throttle setting:
While the engine is "hesitating", give the throttle 2-3 very quick pumps to try to pump in extra fuel with the accelerator pump (returning to the same higher throttle setting). If the engine "takes off" for 1-2 seconds, then returns to hesitating, then that confirms it was starving for fuel...Carburetor rebuild needed.
If your hesitation is only when hitting the throttle for fast acceleration, then that indicates a bad accelerator pump...also needing a carburetor rebuild. When replacing an accelerator pump, make sure to use the green one (silicone) which is ethanol tolerant.
Ray
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"Knot Easy" 2000 Horizon 240 Volvo 5.7GS /SX
tow: 2017 Honda PILOT EXL-AWD
prev. boats:
'87 Chaparral 198CXL 4.3 OMC Cobra
'69 Jetstar 16ft Ski Boat, 115hp Yamaha
'68 Aluminum Jon Boat, 3hp Sears
'64 Water Wings