What could be the problem

Hello, Scan for trouble codes, and anticipate issues with the EVAP (evaporative emission control) system. Also, pay close attention if the vehicle is running very rich (there are codes for this condition that may pop up). Since the issue is moderated by the fuel level in the tank, I would certainly be looking for a fuel system issue, including the EVAP system. That being said, test the fuel pressure at the engine when the fuel pump is running, then see if it drops off quickly when the fuel pump is stopped. It should hold pressure overnight at least.