Nice to meet you.
This is short for it is nice to meet you.
Glad to meet you.
This is short for I am glad to meet you.
Generally, they mean the same thing. When meeting someone (usually, for the first time), it is a positive experience. As such, I am glad has a bit more of a personal touch, I think: you actually refer to a personal emotion of being glad, whereas it is nice is more of a general observation. The difference is subtle, though, and probably most people might not notice it. Compare for instance these two sentences:
It's nice weather today.
I like the weather today.
They roughly mean the same thing, but the second one is more personal. (And of course, if I like weather that is not usually considered nice, they may mean something different.)
Nice to see you.
Short for it is nice to see you, you use this when you meet someone you already know; as a rule of thumb, use meet when you meet someone for the first time, use see when you are acquainted with them.
Nice to found you.
This sentence is grammatical, but it means you enjoy creating someone. If you mean you are happy about finding someone, make sure you use the verb find, not the verb found.
Nice to find you here!
Glad that I found you!
These are both correct uses of find, and express happiness about having encountered someone (at this specific location).
Glad to is followed by an infinitive, so glad to found you would refer to the verb found as we see it in the foundation of a company, the Founding Fathers and the founder of a city. The man who founded a city is not the same as one that found it!
Stretched thin is fine and what you described.
I think an alternative phrase is the simple "you're really busy", or the idiom have a lot on your plate:
have a lot/enough on your plate also have your plate full
to have a lot of work to do or a lot of problems to deal with
I don't want to burden my daughter with my problems; she's got enough on her plate with her husband in prison. Simon can't take on any more work. He's got his plate full as it is.
(TFD)
Example.
Colleague: Sorry for responding late. I had to do XYZ.
You:
1. Don't worry. I know you're really busy.
2. Don't worry. I know you've got a lot on your plate.
Best Answer
"Nice to meet you, too!" is a perfectly fine response to "Nice to meet you."
However, you can't just add "very much" anywhere. "Nice to meet you, very much" would be grammatically incorrect. If you wanted to express intensity, you should say "Very nice to meet you!" (If you add "too" at the end, that would mean that your response matches the intensity of his initial greeting. That's mildly awkward, if you added "very". and he didn't say "very".)
In very extreme circumstances, you might say: "I'm so glad to have a chance to meet you at last! I've been a great fan of your artwork!"