give (someone) something, typically money, in recognition of loss, suffering, or injury incurred; recompense.
payments were made to farmers to compensate them for cuts in subsidies
make up for (something unwelcome or unpleasant) by exerting an opposite force or effect.
officials have boosted levies to compensate for huge deficits
provide (a pendulum) with extra or less weight to neutralize the effects of temperature, etc..