Outdoor Power Equipment and Small Engines - Lawn tractor runs rough

I have a White 1650 tractor with a B&S 16.5 HP engine. If the PTO is engaged and I try to accelerate the engine hesitates and almost quits before finally revving up and going. It seems like it is flooding, but the manual says there is no gas/air mixture adjustment. I have replaced the air filter and pre-filter, the fuel filter, the spark plugs, cleaned all the baffles and sprayed carb cleaner in the carb with the engine running, all to no avail. It only happens when the PTO is engaged. Any suggestions??

The engine is a B&S 16.5 HP
Model: 42A707
Type: 2238E1
Code: 0008095B
Date: 5/29/02

Thanks, Jim

Has to be a carb problem, engine not getting full fuel charge when needed. One easy (unorthodox) thing to do is remove the 5/8" bowl drain nut, let bowl drain, remove air filter and put plastic tube on carb spray can to the end of the main jet nozzle sticking out in the middle of the carb throat and back spray jet. crank engine 6-7 turns with plug wires removed, this flushes somewhat the carb bowl. reinstall bowl drain nut, air filter and plug wires. see if problem persists.
I've gotten by on these model carbs by disassembling, soaking carb 1/2's in dip for an hour or so blowing out with carb spray and compressed air, washing fuel pump diaphragms in gasoline, blotting dry, cleaning inlet needle seat with carb spray soaked Qtip, and reassembling everything. (don't lose the two valve springs in fuel pump)
Current Briggs retail on kit #693503 is $24.90.
hope this helps,
thanks,

Thanks, Glen, for the suggestions. I will give it/them a try and hope it works.
-Jim

Had an old Murry with a Briggs in the shop before the snow hit that would do the same thing when the deck was engaged. The brake safety switch was border line on adjustment causing the engine to shut off and back on that it almost seemed like one of the coils on the twin was bad.

It certainly doesn't seem like the engine is shutting off and then coming back on. When I accelerate, it hesitates as the RPM's slow way down and then revs back up -- more like it is flooding out. But I will check the brake safety switch just to make sure.
Thanks