Thankfully Norwegian has separate words for guilt and debt! It clarifies political language (compare German and Old English, where the words are the same or almost the same: Schuld, sċyld, etc.)
The meaning "debt" of "gjeld" appears to be related to the original Old Norse sense of "pay" for the ON verb "gjalda", and this is still the sense of that verb in Icelandic and Faroese, I believe, as it is, somewhat attenuated, in the related English "yield" (note that "guilt" is not related etymologically and is a uniquely English word with no known relatives in other languages). At some point the primary meaning of "å gjelde" seems to have become "be valid, count as", as with modern German "gelten" (while Old High German "geltan" and Old Saxon "geldan" likewise originally meant "to pay"). Do any of the Norwegians have access to a good historical dictionary of Norwegian that can explain the history of the verb "gjelde"? Is this the result of later Hanseatic influence on the language? Just going through this course there appear to be many words and uses that are influenced by German, and I assume this is because of centuries of domination of coastal cities by the Hansa.