I think it comes from "I give thanks". When we use 'thanks' as an uncountable noun it always takes a form (like news). When we say "Thank you" the word is a verb (as in 'I thank you') and therefore it won't take the 's'.

It’s less of an abbreviation as it is a different form of the verb “to thank”. “Thanks” being the noun form of the word as in “I give thanks” or “You have my thanks”. Native speakers of English don’t tend to think about it in this way as it’s simply just another way to express gratitude. Additionally, being that “thanks” is very short and really only has one stressed syllable, it sounds more natural and casual than to say “I thank you” in conversation. Of course, depending on the person you are speaking to, it may be inappropriate to simply say “thanks” as it can be seen as a lack of respect. In which case, you’re very likely to hear “Thank you” or “Thank you so much”. In the end, saying “thanks” or “thank you” in casual conversation, however, is a matter of preference.

Because we do. All other explanations are just rules to explain it. . Thanking you for asking. Many thanks for asking. :) Thanks for asking.