Are these signs of a possessive partner or just a partner that loves you a lot?

My partner consistently tells me he wants to be with me all the time including living together. Even when I spend time with my grown child he gets antsy. I’m getting the feeling that he acts like this because of possessiveness and not because he says he loves me.
He remarks that I don’t communicate with him enough but when he texts I do reply quickly and sometimes I am the one to text first during the day. We see each other every weekend which consists of Thursday night until mid day Sunday usually.
We went away last month and we’re together for 13 straight days and we get along but he still says when we’re apart during the work week he mentions oh I can’t I don’t like it without you here and I can’t wait for us to live together full-time, etc. etc.
Is this possessiveness or someone who just truly wants to spend as much time with me as he can? The perplexing thing is that he has a lot more friends and family in his area that I do and he does see them on occasion, but he still wants to be with me essentially all the time, even when that means I may want to be with my own family.