격하게 and 아끼다 are seldom used together, so without context it is hard to know what they are saying. 격하다 (adjective form of the adverb 격하게): 1) violent, fierce, vehement 상대는 격한 공격을 시작했다: The opponent went on a fierce offensive. 2) (in emotion) agitated, feel (something) in the extreme; overwhelm 그는 격한 슬픔으로 말을 잇지 못했다: He couldn't speak because of overwhelming sadness. 아끼다: 1) conserve something by not using it freely (돈을 아끼다; 물을 아껴 쓰다) 2) care for, look after, show affection to (제자를 아끼다; 내가 아끼는 사람이야) 3) (in a negative sentence) spare (노력을 아끼지 않다 - spare no efforts) So 격하게 아끼다 probably means someone is caring for someone with unusual intensity or showing excessive fondness for someone. But again, one can't be sure.