The reduced sense resistance needs more current through it, in order to develop the same voltage as previously. Your schematic shows that a component (LT1952EGN-1, U1 pin 10) detects that voltage. (This sort of feedback method is common, although I have no hands-on experience with a LT1952EGN-1.)
As a general principle, it adjusts operation so that it matches a reference voltage. Therefore in order to create the greater current, components are forced to work harder.
It might reduce the burden if you reduce the reference voltage. This assumes the IC is able to detect the reduced voltages.