02 Silverado runs runs very rough when fuel gets low

Just bought a 2002 Silverado PU with V6, 91,000 miles. Every time the gas gets low -- around 1/8 to 1/4 tank, it starts running very poorly. In idle it shakes the whole truck, has no power when driving, jerks and sputters, and constantly feels like it is going to die. But when we fill up the gas tank, everything is fine. We have changed the fuel filter and run injector cleaner through it. But wondering if symptoms indicate there is water in tank, or something else like fuel pump or something? If there is possibly water in tank, how do I get it out?