Engine runs rough when fuel tanks is less than 1/4 full
COULD be something funny with the electric fuel pump inside the tank…I would definitely start with checking the fuel pump pressure at the engine with a fuel pressure gauge you can rent from your local auto parts store.
You might try banging on the bottom of the fuel tank with your fist or rubber hammer next time the engine runs bad and see if doing that changes the running condition. If it does, you have a bad fuel pump.
Other things to look at
1. Bad spark plug wires or worn spark plugs (and is just a coincidence about the fuel level)
2. A vacuum leak under the hood somewhere. With the engine running and the hood up, listen for a hissing noise and any visible rubber vacuum hose that is not connected or cut