The word forgive has been around in English in one form or another for many centuries, but there's been a lot of variation along the way. In Middle English, the word could be spelled foryiven or forjiven, and in Old English it was forgiefan, which still had the same meaning, but also carried additional definitions of "give up" or "provide". This is because the elements composing the word, for and giefan, are equivalents of the modern day words for and give. To forgive is to metaphorically give up a grudge, and that's how the definition got attached. It makes a lot of sense if you think about it, but people rarely do consider it. For, through Proto-Germanic, goes back to Proto-Indo-European per, meaning "before", and giefan traces to the Proto-Germanic word for "give", gebana, which in turn is thought to be from PIE geb, which could also mean "move"
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