Greater string mass will yield higher output from the pickup, lowering the resonant peak. The increased amount of low end, combined with the heavier strings having more momentum makes it more difficult to get clean dead stops when playing staccato passages.
this
I spent years playing .052+ low E strings in quite bass heavy les pauls, and when I tried near standard strings again, the tone improvement was enormous
unhappily, I can't go back too much, since a low .046 string won't hold a drop C# tuning, but it does SOUND tighter and clearer, despite of the string itself being looser
the .052 I use sounds A LOT more boomy, although the string tension is fine
getting the screws too close can also make the bass boomy and distorted