M.P.
I agree with Missy F. He's this way because he hasn't learned how to be with just himself. Sounds like veryone makes sure that they're with him so he won't cry. The focus now needs to be on helping him learn that it's OK to be by himself.
When you leave the room, tell him you're going to the kitchen and will be right back. Keep talking to him as you leave but don't give in to his demand to stay there. Let him follow you if he wants to do so. If he follows you, ignore his tears.
Be sympathetic while continuing to encourage him to be by himself. Perhaps set him up with a toy or two before leaving the room.Tell him that he's OK and quickly leave.
At first make your leaving short. Go back in with him in 5 minutes or so and gradually lengthen the time you're gone. He will eventually be able to be by himself for longer periods of time.
Do not hold him when he's crying. By doing so you're giving him attention for doing something you don't want him to do. Hold him when he's quiet. You could start out holding him before you're going to leave the room while telling him you're going to leave in a sympathetic tone of voice. Make it quick. Leave quickly. Return in 5 minutes and tell him you're back but don't pick him up or hold him. Be matter of fact. Tell him in a matter of fact voice that he's OK.
After you've held him before leaving a couple of times, don't hold him anymore before leaving. Advance to telling him you're leaving and that he'll be ok. Then advance to just leaving.
It will take time and consistency. It is hard to not respond to those tears. Remember, tho, that by trying to calm him you're also giving him the message that he's not OK. Your goal is to teach him that he is OK. It's OK to cry but don't reward the crying. Teach him how to handle his anxiety.