The language of purring
Cats also purr if they're injured, while giving birth - even when dying. British zoologist Desmond Morris has observed that purring is "a sign of friendship - either when the cat is contented with a friend or when it is in need of friendship - as with a cat in trouble. (1)
A cat's purr is a type of language, as is the meow. The meow tends to be a more intense expression than a purr. Although purring can also have emotion effect on cat owners. Purring doesn't always indicate a cat is content, it can mean a variety of things. (2) At the very least it is a way of displaying submissive as opposed to aggressive intention.
German ethologist and cat behaviourist Paul Leyhausen interpreted the
purr as a signal that the animal is not posing a threat. (3)
Purring and attachment
Even if you're across the room, your cat is still communicating with you, and being affected by your presence, which is probably reassuring for him. An interesting test would be to film him while you're out of the house. It could be his way of maintaining a connection with you. It is theorized that kittens and mother cats use purring as a way of bonding and that this may be a form of communication used throughout a cat's life to facilitate bonding.
Kittens are able to purr from a few days after birth. They can purr
while suckling from their mother which may communicate contentment or
maintain contact with her. ... Mother cats may also purr while nursing kittens, perhaps >to maintain contact with their offspring. Or maybe it’s all down to the
hypothalamus detecting a pleasurable sensation and helping to trigger
Possible emotional damage of rescue pets
Contrary to the prevailing view, there is evidence that emotional pain may induce greater suffering than physical pain. Studies have shown that emotional factors weigh more strongly in animals’ behavioral choices than physical pain. (4)
Although it has yet to be determined what the long term effects of psychological or emotional suffering can be; it is becoming more apparent that a history of emotional abuse or neglect may well have lasting effects on a pet's psychology.
Given you got him from the shelter, it might be a huge relief for your cat to have found you, and this could result in him being extra purry. He may well have an underlying insecurity, without knowing his history, he may have been happy with another owner and then suddenly removed, this is conjecture, but the fact he ended up homeless, means he's been uprooted. It would be hard to provide a definitive explanation as to why your cat purrs so much.
What we know for sure is that animals do suffer psychological and not just physical pain, and that emotional abuse and maltreatment may be far more widespread and pernicious than physical abuse. (5)
The many articles I've linked discuss the variable nature of purring. If your cat is in good physical health and as settled as he sounds, it doesn't sound like something to be concerned about.
As for something else going on in terms of physical health, there is some discussion about possible physical health issues that can cause (perceived) excessive purring.
How much purring is too much purring?