Welcome aboard the forum Island 15!
First off, make sure that it's running on BOTH cylinders. The Honda twins can start and run rather smoothly with one cylinder dead. Of course it wouldn't have good power but they've temporarily fooled me before.
The best way to check for this is to start it up and pull a spark plug wire off. If that cylinder is contributing then you should notice a distinct difference in the way she runs. Do the same with the plug wire making sure you protect yourself from electrical shock by using insulated pliers, wearing thick gloves or wrapping the wire with a shop towel or rag. If unplugging each cylinder gets approximately the same response, then it would indicate both are contributing equally.
While under the hood look closely at the timing belt. 15 years is a long time for a rubber belt and it could be dried out and may have stretched a bit after you first ran the engine. It should not have any missing cogs and should be fairly taught between the two pulleys. Excessive sloppiness could allow the engine to jump time. If it is fairly loose, it should probably be replaced.
It could be that you missed cleaning a passage in the carb. Those things can fool you as they have many of us over the years.
Double check your fuel line connections and make sure your tank vent is clean and opens up as it should. An old, cracked line can suck air and starve the engine of fuel. Make sure that the quick disconnect at the engine is properly engaged and locked on tight.
Creatures building nests can cause this as well and checking the cranckcase vent for critter plugs is routine. Check everywhere under the hood for critter damage and this could include mice chewing at wiring.
Something else that MIGHT rob enough power to be noticeable and is not good for the engine would be a thermostat that is stuck open and not allowing the engine to warm up. A cold running engine won't properly burn the fuel and this effects performance. It also allows raw gasoline vapors to enter the cranckcase and contaminate and dilute the engine's oil. NOT GOOD. It can be so bad that you might notice your oil level going UP and the dipstick smells like gas.
Probably the best advice I could give you would be to buy the shop manual. They are available for about $40 from Amazon and it always comes in handy when working on one of these little gems of an outboard.
But, feel free to ask all the questions you want here. We will do what we can to help you figure it out.
One thing I almost forgot is to have you check your prop hub. The engine can run perfectly but if your prop is slipping due to a failing hub, the performance won't be good. Eventually a slipping hub will leave you revving the engine but the boat won't move. With the kill switch activated put the outboard into gear by rotating the prop by hand while moving the shift lever. It doesn't matter which gear, forward or reverse and it doesn't matter which direction you rotate the prop. It's just that you MUST rotate the prop when shifting the transmission with the engine off. If you don't rotate the prop, you could damage the shifting linkage or the transmission itself.
