Did you do it yourself .... or did an electrician do it. I had my basement sump area installed by a pro ... I dont have that problem.
Here are some trouble shooting ideas. Try flipping the breaker switch, while unplugging some high draw items one at a time... seems like your GFI is acting like a circuit breaker. Is all the wiring of the same amperage/gauge of the the GFI and CB. (i.e 20 amp breaker, 12 gauge wire, 20 amp GFI) maybe your over loading it. should be one circuit for your lights one for your return pump then much of the other equiptment can run on another. But IMO all should be 20/12/20.
If no one has figured this out by Monday, i will run it by him on monday when i see him next. IMO there is a problem if your GFI is tripping and not your CB it seems unusual you probably have too much draw.
Sounds like you may need to consider rewiring your receptacles ...
Len