Agree with Briz it sounds very much like you are using more fuel from your float bowls than the pump is able to supply, could be due to blocked filter, failing/not large enough fuel pump, old fuel lines degrading and restricting the flow, a blocked pick up in the tank, choke stuck open a bit, really dirty air filter etc similarly it could also be too large of a main jet in the carb doing the opposite and flooding the motor, hence when you back off the loud pedal it runs as normal.
Just start with the easy stuff and work your way through the (non exhaustive) list. I'd be checking filters first then jet sizes