Engine wanting to die at higher rpms

[myfirstboat1984]

I have a 1984 WellCraft, 19 ft Inboard. The engine runs good in idle and also up to 3000 rpms. When I start getting past that, giving it full throttle, the engine starts to choke. It will continue to sputter and choke as the rpms gradually go farther down, even past 2000, and won't quit until either the engine quits, or I let off on the throttle. Any ideas where I should start looking for problems?