Your bed is home.
When we brought our kitten home, we were instructed to put her in the litter box, and let her explore the house from there. The idea is that she always knows where the litter box is, because that's where her "journey" started.
Whenever something really startled her, she always fled to the litter box. She still fled to the litter box years after we moved (different house, different litter box even).
Our latest two cats had the luxury of getting their own bedroom since we had a spare. Although they now live in the house and don't really use that room anymore; they still run there if something has them scared.
The same seems to be happening for your cat. He explored both new environments starting from your bed, which means that your bed is his frame of reference (when considering the house's layout). He will have a tendency to default to this place when he is looking for a safe spot.
You keep him safe.
Due to his medical condition, you've likely been taking care of him for a long time. From your story, I also read that you take personal care of the cat (who needs a lot of care to begin with), which means that he's likely to seek you out if he needs help.
It's pretty much the same reason why crying children ask for their mommy, their primary care taker (forgoing gender stereotyping, most children tend to emotionally connect to their mother before connecting to their father).
This is somewhat proven by the cat being happy enough to sit on your lap. He doesn't feel safe, which is why he's looking for the safest place (your bed), or someone to keep him safe (you).
You mentioned the cat really doesn't take to your absence well (losing weight), which further proves that he's attached to you (in a way that his wellbeing depends on having you near).
Your cat is scared and/or feeling alone. At least, that's what I read from his behavior. This can be connected to moving house, although I would expect there to be more of a reason (I've seen plenty of cats move house without suffering emotional issues).
It's possible that his medical situation has left him in a position where he relies on you so much that he's lost the ability to be self-reliant.
Was it a sudden change?
If your cat's behavior changes suddenly, with no provocation (such as moving house), consult a vet. Medical issues can make changes to their behavior, and cats can't tell you where it hurts.
From your description, I gather that your cat's behavior hasn't changed suddenly (or if it did, that it was related to moving house). So it seems (to me) that he's behaving consistently needy, which doesn't suggest a medical problem.
Then again, it doesn't hurt to have a vet confirm that it's not medical.
What to do?
If your cat's behavior is indeed learned and not just a consequence from a medical issue, then the only way to get the cat to behave differently is to train him.
It seems to me that the cat doesn't trust his new environment. So I would focus on making your cat understand that there's nothing to be afraid of. There's an old joke that sort of encapsulates how you're supposed to train him:
A man walks up to a gas station attendant. "Excuse me sir, how much does a drop of fuel cost?". "A drop?", the attendant laughs, "you can have that for free!"
The man smiles, reassured. "Thank you sir. Please put free drops in my gas tank until it's full."
It's a stupid joke, but it's on-topic for your cat. If your cat is only comfortable at a given distance from your bed, try to make small increments. Depending on how easily he learns ans gets over his fear, these increments could be measured in yard, feed or even inches.
Sit on your bed and give him a treat. But with every treat you give, throw it a bit further from the bed, and keep incrementing the distance. Gradually increasing the distance means that he has to move around to get his treats.
The key focus here is that you don't force him, because it's his choice to go and get the treat or not.
Suppose he refuses to go any further than past e.g. your chair. Any treat closer gets eaten, any treat further gets left behind.
A - If he stares at the treat, clearly wanting it but being afraid to go there, sweeten the pot by putting multiple treats there. He's clearly weighing his options, which means that it's likely that he'll go there if it's worth it.
If he keeps making progress this way, keep getting him to expand his boundaries by throwing them further and further. Try to always make it his choice rather than your will.
B - If he doesn't stare at the treat, or he makes no attempt to want to go there, walk over to the treat yourself, and see if your presence makes him feel safe enough.
If this has a notable difference, then you should change tactics compare to A. Clearly, it's not the distance from the bed that makes him apprehensive, it's the distance from you.
This doesn't just work for treats. This can be done by placing his food bowl, treats, his toys, ...
Your cat seems to be more fearful than average, which means that it's going to take a while for him to feel comfortable. But keep working at it, making him expand his boundaries. Even if it's inch by inch, that's still progress.
Keep reinforcing this behavior. Some other ways:
- Hide piles of treats in the house. Make sure he doesn't see you put down the treats. The idea that you're trying to convey is that he could have so many treats if he just looks around.
- Amply reward him when you come home. Bring him something special (e.g. a nice piece of fish). If you always come back with a present for him, he won't mind your absence as much (he'll be anticipating the treat).
- Make him re-evaluate his own decisions. One day (without him seeing it), pull your blanket off your bed and put it on the opposite side of your bedroom. Does he now favor the blanket, or the bed? Regardless of his choice, you're subconsciously getting him to realize that he gets to go wherever he wants to go, he just needs to decide where he wants to go.
- Once in a while, pull a Hansel & Gretel. When you leave for school/work, leave a trail of treats as you leave. When you come home, you'll see how far he managed to get. It's even better if the trail has a small pile of treats once in a while (e.g. behind a corner, so it's a surprise).
Good luck with teaching him to trust his environment. It's not a quick solution, but as long as he makes the choices (and you don't force him), there shouldn't be any risk of him regressing.