Hesitates pressing gas

SOURCE: 2002 Impala 3.8l v6 major hesitation

Have someone do a back pressure test on you catalytic converter. I had the same problem and it turned out that my converter was almost completely plugged. I was also getting a check engine light indicating a misfire on cylinder 4. Once the converter was replaced, the problems went away.

SOURCE: 2000 chevy blazer, truck cranks

Does your battery go dead?

SOURCE: 2000 blazer 4.3 hard to start (fuel problem)

Do you have the fuel tester hooked the in the overgrown air valve on the fuel rail in the back of the engine? Or do you have the fuel line unhooked in the back and hooked to the pressure pump? You want the fuel pressure to be in that 60 lb range so if you are hooked into the pressure valve on the fuel rail allowing fuel to go through, then I am betting it is the fuel pressure regulator. To get to that, you have to take the throttle body off and take the plastic plenum that covers the injector packs. On the back of the mount where your six pack of injectors are sits the pressure regulator. If it is faulty then it is dumping fuel instead of holding the pressure like it should.
Get a Chilton or Clymer manual and it shows you in pretty good detail how to fix it. I've done it to my 98 S10 with the same engine.

If you unhooked the fuel line so you are losing pressure from the line back to the pump then I would say your pump is letting fuel back to the tank when it shuts off. My money is on the first possibility though.

Good luck

SOURCE: 1999 chevy blazer fuel pump cycles when key is on

check or replace fuel pump relay

SOURCE: 98 Chevrolet Silverado runs rough at half throttle and past.

try removing the EGR valve and clean inside of it and manifold