Hi tape, I had big problems with my DS stealing when he was 14-16/17ish. It's very distressing, and yes, the breach of trust is awful. It's totally unacceptable, and you are right to want it to stop.
I think you may be over-optimistic to respect each other as adults. That would be lovely, but he clearly isn't mature enough. Kids need to learn to control themselves, and it can be a real problem when you find they can't, especially if you have started to 'let go'. Someone needs to stop unacceptable behaviour... I suggest that you tell him that he needs to stop taking things/money from you now, and that if he can't stop himself, you will no longer be prepared to support him and he will have to live elsewhere. But you have to mean that. Meanwhile, sad as it is, I suggest locking things away.
The allowance is tricky. I would not be giving him an allowance at all - and don't with my own 18yo, who is also in college f/t with a p/t job. But if you stop it now, at the same time as you are telling him he must stop taking money from you, it may feel to him like he is being punished for controlling himself and not taking. I think I would set a deadline and say that you will no longer give him an allowance after X date.
I don't think punishment is an effective parenting tactic at this age. You need your teens to behave well because they are controlling themselves, not because you are 'making' them. I aim to respond to adult teens as I would respond to an adult friend: if a friend took things of mine without asking, I would first try to check there hadn't been any misunderstanding (you have done that already), then be concerned and try to find out if they had some problem and I would also take steps to make sure it couldn't happen again. I might give them a second chance, or even a third, but if it did happen again, that friend wouldn't be coming into my house again... And I think a similar approach is appropriate for an adult son or daughter. If you explain that to your DS, he should understand...
Good luck with it. And don't lose hope: my son stopped stealing from me about 18 months ago, and yours will probably still stop too.