Your the second person this month with that exact problem. The other guy said he replaced the filter and it went away for a few days, then the hesitation returned. He suspected the new filter clogged up.
But to me if it's related the the quantity of fuel in the tank, it could be a pump pick up problem. Also I'd suspect the fuel cap or some other fuel tank pressurization problem related to the emissions system. The tank usually maintains some pressure, and when you first start the engine it does some sort of system check of the valves that send vacuum to the fuel tank to control the pressure caused by heat and fuel evaporating. If the fuel cap is bad you usually get a check engine light. May also get a surging idle.
My 98 explorer had a problem of turning left with less than a 1/4 tank, the engine would stall briefly and suddenly restart. Once it stalled completely and left me facing an oncoming tractor trailer....Not a problem to be taken lightly. We were told by the Ford dealer that Ford had redesigned the fuel pumps in those trucks about 7 times because they couldn't figure out the best fuel pickup design. We put in a new pump which helped, once in a while it still does it.