Could you please explain why the infinitive that means "to be in a position in which the upper body is upright and the legs (especially the upper legs) are supported by some object" is to be sitting but not just to sit. What is the difference between both infinitives?
"To sit" is the infinitive, "To be sitting" is actually the present continuous tense, which is generally used to refer to the act of remaining seated. "To sit" is in the present simple, and it refers to the act of sitting down.
"I sit on the chair" sounds like you're talking about the act of sitting down, while "I am sitting on the chair" unambiguously refers to the fact that you are currently on the chair.