Promise to love her for better or for worse
That's from the vows of a wedding and I kinda know what that means, but I was wondering why did they use 'for' here.
Could you find and show me the same usage of 'for' from any dictionary entry?
"For better or for worse" is a common and very old idiom. It means "under any conditions", as you probably already know.
The expression appears in the poem Confessio Amantis, written circa 1386 in Middle English:
"For bet, for wers, for oght, for noght."
(rougly translated "for better, for worse, for something, for nothing")
It later appeared as wedding vows in the Common Book of Prayer of 1549:
"for better, for worse, for richer, for poorer, in sickness or in health."
Because church services and wedding ceremonies have for so long stuck to the "traditional" wording of this and other books such as bible translations in Early Modern English (eg King James version), much of this older, archaic language has just stuck and found its way into modern speech as idioms. We use it just as we use some Latin words and phrases (eg "et cetera", or "ad infinitum").
Treat it as an idiomatic phrase rather than examine it with the rules of Modern English.