compensate

To compensate someone is to give them something, mostly money, to make up for what they lost. The airline compensated her for the case that never came off the belt.

That sense takes a person as its object and FOR before the loss: they compensated the family for the delay. The other half of the word has nothing to do with money — to compensate for something is to balance it out, so a driver with poor night vision compensates by going slowly, and a weak left hand compensates with a stronger right. The noun is compensation, which in British offices also means the payout itself. Compensating and overcompensating carry a whiff of psychology: someone very loud about a thing may be covering a gap. The preposition tells you which sense you are in — you compensate a person, but you compensate FOR a weakness.