You say you had to fix the recoil starter - that means the previous owner didn't maintain the motor properly and just yanked it to death trying to start it.
First thing is to check for a good strong spark on both cylinders. It could also be dropping one cylinder when it revs (stronger spark is more likely to arc through bad insulation); if the plug wires look old/cracked they should be replaced. Make sure the points are set correctly so the timing is right and the plugs are correct for the motor. Also clean the carburetor and make sure all the gaskets/packing is good.
First thing is to check for a good strong spark on both cylinders. It could also be dropping one cylinder when it revs (stronger spark is more likely to arc through bad insulation); if the plug wires look old/cracked they should be replaced. Make sure the points are set correctly so the timing is right and the plugs are correct for the motor. Also clean the carburetor and make sure all the gaskets/packing is good.