ORIGINAL: ********nut
Have you watched the fuel line while the engine is running? Is it getting gas, bubbles in the fuel, etc. Have you checked to make sure that there are no cracks or holes in the fuel lines? Remove the fuel line and exhaust line; blow through one while holding your finger over the other to see if the lines and tank will hold the pressure. If you continuously have to blow in the line; you have a leak somewhere. If that is the case; replace your fuel lines and make sure that the tank is not leaking at the stopper or if there is a hole in the tank.
I'm going to second ********nut's advice. 90% of all "engine problems" generally trace back to fuel tank and/or fuel line problems. I had problems with my Tiger Stick a few years ago similar to what is described here. I would start it and it would run fine up to about half throttle. Once I moved the throttle past half way, the engine would rev up then start to sputter and die.
I took the plane home and checked the fuel lines and tank. It turned out that the clunk line inside the tank split. The engine could draw enough fuel up to about half throttle, but anything over that was too much pressure for the split fuel line and it would open up and not draw enough fuel to accelerate.
No amount of messing with the high and low needles will fix something like this. You bought the plane used and you have no way of knowing how old the tank and lines really are. The plane could be fairly new, but the owner might have re-used a tank of fuel lines from an older project. If you can't test the tank and lines completely to your satisfaction, it will only cost you about $8.00 to put in a new fuel tank and fuel lines.
If you get the same issues with a new fuel tank and fresh fuel lines, we can go from there.