The 39mm carb is the “correct” size for a 125 shifter. I use quote marks because in IMHO this means it is wildly oversized unless you know what you’re doing and are running at or near the kart’s maximum potential. Otherwise, the engine will seem sluggish and too rich. This is one of many reasons it’s usually not a good idea to start out with a shifter kart–the carb is not forgiving for those at the beginning end of the learning curve. The cure for what seems to be a carb problem often is to stick your foot in it and to drive faster, which may mean driving over your head.
The pump around system is one approach to curing a perceived issue with the float sticking in high-g corners–the kart sees g forces that are unobtainable on a bike. A lot of very fast shifter drivers that don’t believe in pump arounds and do fine with floats.