The crossword solution for the term 'weaken insidiously' is 'UNDERMINE'. To UNDERMINE something means to weaken it gradually and subtly, often in a way that is not immediately obvious. It can be used to describe a person's actions, such as when someone tries to damage another person's reputation or credibility without them realizing it. It can also be used to describe a process, such as when a company slowly erodes its competitors' market share.