The title was meant to be ironic.
I discussed this with my wife who is, as always, far more insightful than I. Her thought about this conversation was, “This is the way this person deflects responsibility; By creating drama that takes focus off what’s really going on, or have set in motion, because they have not acted responsibly and are now experiencing pangs of guilt as a result.”
Knowing this person as well as I do and for as long as I have, I’d have to agree.
This really depends on the relationship between the people involved.
I think asking a simple how are you and making yourself available should suffice without making the person feel defensive.
Well, let me ask you this. At some level, were you thinking that the person involved actually is kind of a fuck-up?
Nope. In fact less than two weeks ago I commended the person for having accomplished something not insignificant and said how proud I was, without reservations.
So, no. Not a “fuck-up”. But a few poor decisions were made in the the interim and said person should really own up to them and course correct instead of kvetching and shifting blame where it doesn’t belong.
I hope those following along have gathered from my tone that the person is still quite young; A young adult to be very specific.
I think you left out “Thank you for your concern, but please mind your own business.” Unless you’re a close friend of family member (and maybe even then), it sounds condescending and presumptuous.
To hear those questions once, or once in a while, no problem.
Hearing how tired I look for the tenth time today, or every time I see my mother, could get a little snark in return.
Don’t take this the wrong way, but why don’t you and your little irony meter friend go take a long walk on a short pier. 
How dare you, sir?! 
Good, because if you actually ever approach someone with “don’t take this the wrong way, but…” then you immediately set them up to feel defensive about whatever comes next. This is not a good start to any conversation, unless your goal is to deliberately create a hostile interaction.
I think all of your questions would benefit from a more empathetic approach.
Instead of: You seem kind of upset. Did something happen?
How about: This is one of those days when I feel like punching the wall! How about you - good day or bad day?
Instead of: Are you looking after yourself? Eating well?
How about: Ugh, I suppose I should go to the gym after work today, but I really find it tough to balance work with good health habits. Frankly I just want to go home and eat a croissant. You seem to be managing okay - any tips? Or do you find it as hard as I do?
Instead of: You seem like you’re stressed or overloaded. Are you getting done what you need to get done?
How about: Whoa, I hear the boss assigned you to the Smith account on top of the five other accounts you’re managing. Are you okay with that? It would drive me crazy if I had to deal with that!
Instead of: Maybe try getting in the gym? Might help you manage the stress better.
How about: Damn, have you found any good ways to manage stress? I go to the gym and I guess that helps, but I’m curious what other people do, because it is still a struggle for me.
Instead of: You seem defensive. What’s bothering you? Is everything okay?
How about: Oops, I think I might have overstepped some boundaries. I apologize. But I’d like to talk if you would. In your shoes I would probably be struggling to remain gracious about that meeting yesterday. What’s your take on it?
Thanks, CairoCarol, for the thoughtful advice.
I realize now I could and should have been more diplomatic in asking the questions that I asked. I can be a bit direct when I’m caught in the wrong moment and simply want to cut directly to the solution because what I’m hearing sounds like a problem instead of a venting.
The person in question knows me well and now understands my reaction. I don’t think there was any long term damage done. Just a temporary annoyance with me is all it caused in the end.