The girl sounds like the immature one in this situation...either way this was far in the past and lots of adolescents go through difficult situations like this - as have I.
I cried in front of my first serious girlfriend, and admitted to having suicidal thoughts as well...we split up soon after for unrelated reasons but the important thing is that she didn't hold it against me or call me "weak." This girl's response to the situation was anything but appropriate. I'm sorry you've had a run in with such an awful, immature, mean, spineless girl.
No, girls aren't rejecting you because you're "weak." Being an "Alpha" at 16 is a far cry from being and "Alpha" (which is a term I hate) as an adult. Honestly I can't think of anything more weak than a man who refuses to acknowledge his feelings - you've developed a certain strength by going through what you did...now you need to put it behind you - you have every capability to overcome this. I recommend doing some reading on "The Looking Glass Self" to better understand how you self perceptions can lead you down the wrong path. If you don't carry yourself with confidence out of a self-perceived "weakness" it may effect your ability to attract girls, but this has less to do with you actually being "weak" and more to do with the fact that you let these false ideas drag you down, that you carry this with you wherever you go. This whole event only has as much bearing on your self-image as your thoughts allow it.
If this girl really was able to turn your peers against you, and still is, then she's the weak one, and your peers are likely immature twats. And if they are, don't expect them to change, and don't look to them for validation either.
I take it from your post that you live in a small town? If so I strongly recommend saving up some dough and moving somewhere new. Get a fresh start somewhere new, acknowledge the past, accept what you've learned from it, and put it behind you. You have a whole life ahead of you, stop wasting it by being surrounded by mean, immature, jerks.
It gets better.