What am I? Feel welcomed to answer

Question

Hi!

I am big business you should better not skip

If I'm used longer you're in a relationship

Also, I feel odd when there are 2k human beings

My absence might hurt anothers feelings

Who/What am I? Can you figure it out?

Answer 1

My guess is

A Handshake

I am big business you should better not skip

Even the biggest of businesses follow the norm of a handshake greeting. (unless another norm replaces it, like Japan's bowing greet, but even that one can include a handshake)

If I'm used longer you're in a relationship

A prolonged handshake turns into hand holding, a common gesture of couples.

Also, I feel odd when there are 2k human beings

Greeting a crowd is normal, but handshaking a crowd can be quite awkward

My absence might hurt anothers feelings

A first meeting without a handshake might be considered rude to the other person

Title:

We are welcomed to try, which hints to something done as a greeting, also hinted by the Hi! at the start of the riddle

Answer 2

My guess

hospital(ity) (or patient?)

I am big business you should better not skip

A robust civilisation should have a hospital of some kind to treat patients

If I'm used longer you're in a relationship

If you are in a hospital for long while, then it probably means you need to go there often; you have built a sort of relationship to it.

Also, I feel odd when there are 2k human beings

This could refer to the recent pandemic

My absence might hurt anothers feelings

Lack of hospitality (or patience) could hurt people’s feelings.

Answer 3

My guess:

identity

I'm not too sure though.

1. I am big business you should better not skip

   I believe this refers to either "corporate identity" (establishing a brand presence) or how corporations are utilizing personal information (i.e., identities) for targeted sales.

2. If I'm used longer you're in a relationship

   Refers to how mathematical relationships (or functions) with identities have been studied for longer.

3. Also, I feel odd when there are 2k human beings

   In a large crowd, one might feel a sense of loss of identity.

4. My absence might hurt anothers feelings

   I think this refers to an algebraic structure without an identity element (where some theorems break down). Or the absence of an individual (or their identity) may upset someone else.