carb issue

I just bought a 1997 Ski Nautique 176 with a carbed PCM 351 in it. I had been looking for one for a while and finally found one in good condition with low hours, but it seems to be having a problem with the carb. It runs great at idle and plane speeds (above 2500 rpm), but it dies out anywhere between those. Any suggestions on what might be going on and how to possibly fix it? Thanks!

I won't actually run long enough to tell the difference really. Even if it just rev it in neutral within that rpm range, it will rev then sputter and die within a few seconds.

The accelerator pump seems to be working. When I open the throttle, I can see it injecting fuel into the carb, but after that initial injection, it stops, which is what it is supposed to do as I understand it (but I'm not expert).

Ok, here is a better description, maybe.

Once warmed up, it starts fine just at idle. To cold start it, I give it about half throttle, and once it fires, I immediately bring it back to idle. To get to planning speeds, I have to give it about 3/4 of full throttle to get it going without dying and then can back it off as long as I stay about about 2500 rpm. Basically, I can't slowly increase the throttle from idle because it will initially start to accelerate for a couple seconds then sputter and die.

Adam,

If you just picked up the boat, I would go through it completely. Change fluids and do a complete tune up. You haven't said what ignition you have. I assume it's electronic so plugs, cap, rotor and set the timing. Then run it and see what we have for a baseline. A tune up can do wonders.

The engine is not a Pro Boss. The distributor sits on the top of the engine toward the front. I did just get the boat, and I am in the process of going through and doing maintenance and finding issues. I am a complete novice in DIY engine work, so it's a working progress. Thanks to everyone who is providing input, I appreciate the help.

If the advance springs were broken, the weights would go to full advance & stay there. I think it would not idle nor restart well after that. You also would be getting some backfiring.