Your baby is so smart-- he knows you are his, and he is yours, and he knows that you are his favorite person in the entire universe!!
I think your little guy is going through another normal phase of separation anxiety. Those phases comes in spurts in those first years of life, continuing on and manifesting in different ways as they grow and develop. It's not that he is regressing or going backward in any form, he is just at a new level of awareness that you two can be separated, and he feels most comfortable and safest emotionally and physically when he is with you/on you.
All five of my kids went through this in many forms. My youngest is 18 months old right now, and is in the thick of what you describe. He wants Mama nearly 24/7. If I leave the room, he whimpers and scuttles behind me, asking to be picked up. He's afraid I'm walking away and he's not sure if I'm coming back. So, I meet him where he's at-- I turn around and say the words for him that he can't say yet: "Mama's here. Do you want to be held? It's okay, Mama's not leaving you. Everything's okay." I hold him while I do whatever I'm going to do, unless I absolutely can't hold him. After awhile often he wants to get down and go back to his fun, but only if I immediately address his fears and let him know I'm there for him. Sometimes we spend the whole day glued to each other. As much as I am able when he's needing this kind of attention, I give it to him, putting other things on the back burner. The phase will be gone shortly. I've found with my kids that the more and the sooner I fill that emotional need, the sooner it goes away. I think if they sense that we want to hurry up and get through it, it all lasts so much longer.
In the end, filling this need will create a really secure baby/child-- that's the good news. He will be confident in the people he loves, that when he is in need, they are there, not only for physical things, but for the even more emotional needs that he has. He'll go on to be able to generously love others and help them as they need help. In our culture, filling the emotional needs of wee ones hasn't been stressed as important-- filling the physical needs has, and we're all pretty good at that, but the emotional needs are often thought of as not-as-important. I think this is erroneous thinking. If we fill those needs when our kids are small, they will have the tools they need to step ahead and move on to become giving, caring, dependable older kids and adults.
It's hard, isn't it? It drives me bonkers some days when my little guy just wants me to only hold him. It's especially hard when we have a million other things to do. But I have to stop and remind myself of the things I know to be true, and to apply them to his needs. I find ways to just delight in him while we are velcroed together-- he is so beautiful, and playing peek-a-boo with him is so delightful, and this baby time is sooooo fleeting, and tomorrow he will be an 12 year old. So I remind myself to revel in this time with him. When he's 12, he won't want to hang out with his mama anymore, and I'll wonder how it all went so fast.
Think of it as your babymoon-- it will disappear so quickly, and his needs will change.
Hang in there, Mama. You're doing a wonderful job. He's a lucky little boy to have you.