From fridge, bring to room temperature (about half an hour) before serving. If at room temperature it is still too thick, yes mix a little water in - probably by hand is enough, so you won't have to go through the transfer to & washing of processor.
It is often served warm (from just being made) in restaurants. You could do that with a quick warm up in microwave or oven.
I appreciate the help. I've made loads of hummus and it's never tightened this much. Good point about the addition by hand. I hate dirtying the food processor!
I agree with Nancy's tips, and would add that when my hummus tightens up in the refrigerator I often add a bit of Extra Virgin Olive Oil before serving.
I always add more lemon juice, which brightens it up nicely. You can just stir it in with a spoon. (I make triple batches of this recipe, freezing in pint and half pint containers so we always have it on hand. I know exactly what you're talking about.) ;o)