I have a Simplicity with a model 9 engine on it. It was advertised as 3 hp.
Back in the Spring we went through similar problems with it. Two things you can check:
the air bleed to the float bowl goes through the gasket between the top and bottom halves of the carb. Its the hole offset in the little tab on one side. If its getting any air at the gasket the carb. will not feed properly. Try sliding a .002 feeler gauge in by the gasket at this point to see if its tight.
The other problem was the condenser had apparently failed, There was lots of sparking at the points. Ran fair at idle, reved up it would skip and sputter. A new condenser and points greatly improved the operation of the engine. Not Cheap, though. I think the points were $45-50 and the condenser was $20 or so.