I felt my resistance weaken and at the end I allowed her to stay for one night.

weaken 是由形容词 weak（虚弱的、不够坚定的）加上后缀 -en（使变得……）构成的动词，表示"使变弱、使动摇"。在句中指"原本的抵抗/决心逐渐变得不那么坚定"的过程。