Sticking Intake Valve?

Don't know anything about configuration of this model by number, but I can recommend you hit up your library for a copy of "How to Repair Briggs & Stratton Engines", by Paul Dempsey. I have 2nd edition, but I think they are currently on fourth edition.

First thing I would do is pull the head and inspect the valve seats. Lap the valves if necessary. If the valve seats are good to go, then you have to look at the lifting mechanism. Does it have rocker arm, or straight push lifters? Could the cam shaft have been damaged (i.e., have you hit any stumps with it)?

Weird that it runs better under load. Try spraying carb cleaner into the carb while it's running to see if it can remove some carbon build-up or whatever might be causing the lifter to stick. Be careful about how much you spray..too much and the engine will shut off. Spray it until it sputters, let it recover, then spray some more.

Check the spark plug. A badly fouled, improperly gapped plug can cause similar problems. Of course clean/replace the air filter.

Are you sure that the valve is sticking or is the carburetor flooding?