First, I want to say this - no, crying is not being weak, it's not a weakness. That's just a propaganda coming from the same place as sexism and homophobia and racism. Personally I think it's more connected to believing that showing your emotions, any kind of emotions to others means other know something personal about you and that can be exploited, therefore it was viewed as weakness to cry but also went into sexism saying stupid shit like "boys don't cry" and all that stupidity, just another way and another thing to shame people for in order to control them and undermine them oppress them. Please don't listen to that bullshit.
Here's what I've discovered about crying from my own experience. I never cried when I was a kid, not really it wasn't because I was ashamed but rather because crying meant admitting to myself that I feel something powerful enough to make me cry and I never wanted to do that. When I was 13, I was at some of the worst times of my life it was then when I couldn't deny the severe depression and loneliness I felt anymore. I started crying, alone at night. And every time after crying I would calm down and feel WAY better, I was still lonely and still depressed but somehow I felt like I could take it and I could deal with it. Somehow after crying I would feel way stronger. I started crying every time it would get too much pain which was every night. Soon there were only times where I wanted to cry all the time and had to fight back tears and wait till I was alone at night again because I don't want other to see, not because I was ashamed but because I didn't want the questions and fake compassion to deal with. I cried every night and every time I was alone and the truth is that is the only reason I got through many many years of terrible suffering and survived.
I also read somewhere that when a person cried the body releases natural pain killers,which is why I felt numb (which was a welcome change of pace from the pain) sometimes after crying I guess and I used to get very serious headaches very often I mean like literally every other day and crying even stopped the headaches when nothing else could, no headache pills ever helped me.
I'm 22 now, and I think I haven't cried well in 2 years at least now and I feel weaker than ever, and that's the thing, I can't bring myself to cry because I feel weak, I'm scared of facing the pain that makes me want to cry I'm afraid I can't handle it and I don't even know how to start. So I feed myself distractions like watching tv or eating my pain away to get away from my thoughts and feeling and it's ruining me completely. No, I want to cry, I want to cry to face my feelings and be strong again. And I'm trying, I really am.
I'll finish this with this, people cry because they concentrate on something that is painful(or sometimes happy but I'm guessing happy crying is not the kind we are talking about right now) and they feel the pain, it takes a coward to run a way from them and distract yourself with something else just to stop feeling and thinking and not to cry, it takes an extremely brave person to face the pain, to feel it, to live it and to go through with it. That's how we deal with pain sometimes in a way, we feel it and go through it and we cry because that's expression of that pain and expressions our feelings always good in mental, emotional and even physical way. Keeping it bottled up is not healthy in any way and avoiding pain is definitely not bravery. Crying is good, crying is brave.
Also, google it, why crying is good for you, I'm sure you'll find lots of actual medical reasons why it's good for you including your physical health.
Good luck, and have yourself a good cry, I'm thinking of you and I'm with you.
I hope I'll cry again too.