The idling and the bogging may or may not be related, so you have to treat them as different problems until otherwise.
1. As simple as this sounds you always start by running it off of a different fuel tank, like a small plastic portable tank. Half the time there isn't anything wrong the motor itself, but rather something wrong with the boats fuel system. This can be a pinched or collapsing fuel line, bad or old gas, or a bad anti siphon valve. Marine engines are very sensitive as to the quality of the fuel, and if any part of it is over 90 days, the fuel itself is always going to be suspect. This is a pass or fail test, and the engine is either going to run better or it is not. If it does run better, on this portable tank, first change the anti siphon valve and retest with the engine hooked back up to the boats fuel tank. If it goes back to running poor on the boats fuel tank, that tank will need to be pumped out. Bad anti siphon valves are a common problem, when they go back they create a blockage and restrict the amount of fuel that flows to the engine. If the engine does not get enough fuel it obviously will not make full power. Click this link, this explains more on the anti siphon valve and why they go bad. http://www.sterndrives.com/anti-syphon-valve.html. On this anti siphon valve there is an inlet side and an outlet side. The inlet side faces the fuel tank, the outlet side faces the fuel line. When the engine runs, the fuel pump creates suction. This suction pulls the check ball off of it's seat and fuel is allowed to flow around it. The problem with this is over time the spring in the valve will get weak or simply break. When that happens the check ball will be free to jump to the outlet side of the valve and create a blockage/restriction on the outlet side of the valve. If the spring is simply weak and not broken, this will more or less happen at random. Click this link for a picture, it will make more sense once you see it Http://imgur.com/a/tpq4H. The anti siphon valve itself is located at the fuel tank, where the fuel line connects. If you pull the fuel line off the tank you will see a hose barb, that hose barb is the anti siphon valve.
2. If no change, then compression testing the engine is next. Your results need be about 80 psi or better on that engine, all cylinders should be within 10-15% of eachother. If you get below 80, then the engine is worn out or has stuck piston rings. You might as well stop your troubleshooting here, as there is nothing you can do to an engine with low compression to make it run better. From there you would decarbonize the engine by running a product like Seafoam through it and then re-testing the compression and see if it comes back up or not.
3. Spark test Get a timing light and run the engine and hook the timing light up to each plug wire one at a time and see if the timing light flashes or not. Flash means the engine is sparking when running, no flash means no spark. Again this is a pass or fail test. If there is no spark on an cylinder, change the plugs first and see what happens. If spark does not return, swap a firing coil for a non firing coil, and see if the problem follows the coil or not. If it does, there is a bad coil. If the lack of spark stays on the same cylidner, there is a bad powerpack.
4. Hook up a fuel pressure gauge between the pump and carb, measure fuel pressure with the boat going as fast as it can. Pressure needs to be at least 3 psi. If it's low, the fuel pump is weak. Make sure you do this after you do #1. If that anti siphon valve is bad that will cause low fuel pressure because the fuel pump would be struggling to pull through that restriction/blockage that a bad anti siphon valve creates.
5. Lastly, if you do all of the above steps and still do not get any kind of result, the problem is going to be in the carb. They are either dirty on the inside, or one of them has a sticking float not allowing fuel into the engine. in any event if you get to this point the carb would need to come off and be rebuilt.
If you are looking to do some of this yourself but do not have the tools, places like autozone will give you free rentals on the tools. You basically pop a deposit down on a credit card, borrow the tools, and if you return them in 1 piece they give you the deposit back. The last thing is when you troubleshoot you specifically want to do it in this order. If you jump around you will miss things or make mistakes. This is the most time effective way to figure out what exactly is wrong with the engine without wasting time or spending money on parts you do not necessarily need. Does that all make sense. I do want to make sure you are happy with my service before you go. If you had a further question on the issue by all means feel free to ask. If not, Just in case you do not understand the way the website works (and some folks do not). You do have to put forth a positive rating in order for it to credit me for helping you. When ratings are not done, the website simply keeps your deposit and they will not credit me. The ratings box is located at the top of the screen. To rate, you must select the star you wish and also confirm it. Please let me know if you run into any problems or errors when trying to do it. If you do have a problem, or if you can not see the ratings box which is at the top of the screen. Please reply back "I rate Jason's service _______" and fill in the blank.
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Thanks in advance, and good luck