Thank you, Mister Micawber and Marius Hancu, for your
comments.
So:
1. I will meet up with you means I will meet you after I finish with what I am currently doing.
2. I will meet you means Let us agree to
meet.
3. I will meet you up is unnatural unless 'up' is
used to point to a direction or a place (e.g., I will meet you up there).
However, I did forget
to ask of the fourth usage: I will meet
with you. Therefore, I decided to google "meet with" and found
the following interesting paragraph to share with you:
"Meet with is a Standard idiom (I hope to meet with them next
week), meaning “to hold a meeting, an encounter,” as distinguished from I
hope to meet them, which could also mean “to be introduced to them.” Meet
up (I hope you and I meet up again some day) is Casual at best,
possibly dialectal. Standard users would use only meet at higher levels.
Meet up with, however, is at least Conversational, and at least one
dictionary considers it Standard; it simply means “encounter,” as in I hope
to meet up with her again some day."
([link]
Best