If the petcock is suspect, you could test it by removing the fuel lines and attaching some longer tubing that drain into a gas can on the floor. Alternatively, connect lines to the float bowl drain ports and open the drain screws (I prefer this as it also shows if the float valves are opening, but fuel flow will be less dramatic). Then apply vacuum to the side port on the petcock with a mityvac, a syringe connected to line, or just use your mouth. It should flow gas very fast on both hoses with even a small amount of suction. Look for particles in the drained fuel. If gas barely comes out, or none at all, then double check that the shutoff valve on the petcock is turned fully ON. If flow is still weak, remove the petcock from tank and check if anything is blocking the screen and for any debris inside the valve.

Is there any rust inside the gas tank?

Also check the short hoses that run straight up from the carbs and plug into the airbox, right under the air filter 'plugs'. Those are vents for the carb slides and MUST allow air to enter and exit from OUTSIDE the airbox. If those ports are restricted or completely blocked off, the slides will not operate properly and the engine will only run well at idle speeds.