Separation anxiety already?

My son turns 8 weeks in two days and lately he’s been extra clingy. He only wants to be held by me, he even cries when his dad holds him. Luckily I have the next month off to try and wean him off of me. I hate to just let him cry in someone else’s arms. When I’m in the same room he’ll look at me and slowly make the saddest face and then start crying it breaks my heart. So I try to stay away but I hate hearing him cry from the next room. Any ideas? Or is he too young to have this sort of problem already and it’s just in my head?