The engine needs 3 things to both run and make full power. What it needs is compression, timed spark ignition (spark happening at the right time) and the proper ratio of fuel to air.
When I get engines in the shop that do not make full power, this is what I do to troubleshoot them, I also do it in this specific order in order to both be thorough and keep from making mistakes.
What I start with is engine compression and spark tests.
1. Compression test. Results need be 100 psi or better, all cylinders should be within 10-15% of eachother. If any cylinder is under 100 psi it is either worn out, or has a valve problem, and the heads will need to come off and the valves inspected next. A healthy engine will read in the 140 to 160 psi range.
2. Spark test. The easiest thing to do here is to hook up a timing light to each plug wire one at a time and see if the light flashes or not. Flash means spark, no flash means no spark. No spark can be something as simple as a bad spark plug, that was dropped on the floor before you got it, or a bad plug wire. If you get no spark on any cylinder then the engine is not running on all cylinders. Most people will elect for a tune up at this point and replace the cap,rotor, plugs and wires.
3. If compression and spark are good, make sure the fuel filters are all changed. Some engines will have up to 3 fuel filters on them. With 1 large canister filter in the front, followed by paper filters in the carb and fuel pump.
4. Next is to get a small outboard tank (like a 3 gallon) and fill it up with known new fresh gas and try it. If the engine runs better on the portable tank there is an issue with the boats tank, this can be a blockage or air leak in the fuel pickup and related hardware on the boats tank and related lines.
5. If no change, next is to hook up a fuel pressure gauge between the pump and carb. Fuel pressure needs to be in the 3 to 7 psi ballpark at max speed. If it's not, the fuel pump is weak and needs to be changed out.
6. Lastly, if you got this far and the engine STILL is not running correctly, everything else has been ruled out at this point, and the problem is inside of the carb. The carb will need to be either rebuild, or replaced (depending on how nasty it looks inside)
If the troubleshooting is done in that order, and no steps are skipped, the root cause will ultimately be found. Also keep in mind there is always a chance there is more than 1 thing wrong with the engine. So if for example if you pull apart the fuel pump and change the filter inside of it, and it looks nasty but the boat still does not run correctly, try not to get discouraged. The older the boat is the odds of it having more than one problem goes up. I couldn't tell you how many engines I have worked on that have come in and the boat has bad gas in it, all the filters are trashed, the ignition system needs a tune up, and the carb is clogged as well. It definitely does happen.
Does that all make sense to you? If yes, do you have any other questions on the issue?