From Longman Dictionary of Contemporary Englishweak momentweak momentPERSUADEa time when you can be persuaded more easily than usual Dave caught me at a weak moment and I lent him £10. → weak
Examples from the Corpus
weak moment• For a weak moment she almost relented.• Indeed there are no really weak moments vocally, although I am not convinced by the style of all the vocal cadenzas. 