Late 80s early 90s BF100 troubleshooting

Hi guys, I'm looking for some help with my older Honda BF100. I'll start with the first problems and work up to what the new problem is... I just recently traded my 2007 5hp honda outboard for this older BF100. Before replacing the worn old carburetor, the engine would not idle unless choked, but did open up and run smoothly at full throttle. However, during the last fishing trip, the engine began to sputter and would no longer run properly at full throttle. Since then, I have replaced the carburetor, for the old one was in rough shape, as well as replaced both spark plugs. With the new carburetor, the engine starts and idles properly, but still spits and sputters when opened to full throttle, only putting out about half the power that it should. I have not yet checked the plug gaps, which I plan to do this evening, but does anyone have any idea of what the problem may be otherwise? Thanks

Make sure that the timing marks are aligned properly. If timing belt skipped a tooth, that would cause it to run like there is a carburetor problem.

Mike