If you saw a young lady crying, waiting to board a plane,

No, probably not.

Probably not.

If I were crying publicly I would not want to be bothered by a stranger.

Young, old or middle aged no I would not react to it at all. And I hope other people would be polite enough to do the same back to me.

Exception maybe: like a twelve year old who appears lost maybe but only maybe. Just my luck she is lonely about traveling alone and is on my plane and I end up being her buddy for the trip.

If I'm crying, please just leave me alone.

If by "young lady," you mean a child, and she is alone, then yes, I think you should check to see if she needs help. Ditto for a boy child.

But an adult, or even a teenager ... please MYOB.

No. I too have been that person and would not appreciate being approached. Unless someone appeared to be trying to make eye contact, I'd leave them be.

I'd offer them a Kleenix, and read the situation from there...

Yes, I absolutely would gently ask if she (or he) needed something, and if no, I'd just walk away knowing I had tried to offer assistance to someone who was clearly in distress.

When my mom (and most recently my dad) were gravely ill and dying, and I was desperately trying to get home in time, I found myself both times in the airport crying and alone. A kind word form anyone would have been very welcome. I think everyone has had a moment like that. I usually respect people's privacy but I imagine if you are upset enough to openly cry like that, you may have a problem. Maybe you need to borrow a phone to make a call, or maybe you just need a small assurance that it'll be ok.

This, exactly. 

I asked something similar a few weeks ago here (not about a plane, though) because I had experienced a few times where I saw people alone and crying, either in restaurants or on the street. I have decided that I would probably say something like, "Can I help?" and maybe put a hand on their shoulder. And then I would probably say something like, "I'm sorry for whatever is troubling you." Maybe that would cheer a person up.

No I wouldn't because if I were the one crying I would want to be left alone.
Not only that but in cold weather, my eyes water profusely and will water for a long time. Many times I have tears pouring out of my eyes making it look like I'm crying when I'm really not. It's embarrassing and I'd hate to have anyone call attention to it.

This was me exactly, people acted like I had the plaque, no one would even sit anywhere near me, avoided me at all cost.   The tears were falling silently down my face, there was no stopping them.  It wasn't like I was a loud mess if that makes sense.   

yes, I would and in fact, I have. A woman was crying because she was going to see her sister for the last time before she died. she couldn't get any money out of the ATM and she was bawling in the middle of the airport-everyone was walking around her and it made me sad. I asked her what was wrong, she told me and I helped her with her ATM card so she could get money-I told her that if I couldnt get the card to work for her, I would just give her some cash. she was SO thankful-I forgot what the issue was or why she needed the money, but I saw what she was doing wrong and helped her (she didn't give me her pin, I think she was putting the card in wrong-she was an emotional mess and wasn't thinking right) she gave me a HUGE hug in the middle of the airport for the longest time and said she would never forget my kindness. 

it was one of the best days of my life, actually. It was a huge honor to be able to provide a tiny bit of comfort to a complete stranger-perhaps she can do the same down the road for someone else.

it was actually at least the second time that happened. Once I overheard what was wrong-it was a single mom with two small children. One was obviously very ill and she was trying to get a prescription for him. her insurance card was denied and she was crying her eyes out in the middle of the pharmacy. again, everyone ignored her. she didn't have the money to pay and she really needed the meds for the sick little one. I paid for her prescription and she asked for my address to pay me back. she never did pay me back but I don't care-I told her not to-just pay it forward when she was in a position to help someone else.

It makes me sad how many people don't want to get involved-I might embarrass someone by asking if I can help but IMO, not saying anything is far worse.