I also sense weakness, I was in the Marines, and my impulse is also to be tough with "weak" people, but in a avuncular helpful way, leading them to be stronger. You have to give them queues that you're on their side even as you're not putting up with the bullshit. In the civilian world you have less room to do it and you have less of a standing to involve yourself even if you think you ought to. If someone doesn't like my tougher approach, and it becomes a problem, I transform into being the polar opposite, overly nice, very careful with that person. I don't think this would help them, but I can at least build a personal relationship with them that works.
I'd be proud of someone, whether I had anything to do with it or not, if a weak person stood up for themselves. I think bullying just makes weak people even less self confident and even weaker.