Pets during Pregnancy!

So, my dog, he's about 12, acts SO weird around me now.

If he's on the floor, walking, he just prances around, grabbing at my pant leg, wagging his tail.

But if he's sitting next to me, or on my lap, he's limp. Almost like a ragdoll. He stares at me, falls asleep in my arms & wants to lay next to my belly.

My grandmother gets worried, with him being so old & not active, but he only acts like that when he's next to me.

Should we be concerned, or is he just really being cautious & loving about the baby on the way?