I worry about these things too, sigh. I wish I had a good, one-size-fits all answer, but I guess I do have a pattern. It's more about how I feel about the person than any set amount of time or dates.
I will leave my profile up until I know I really like someone and I feel uninterested in meeting someone else, or if we've talked about commitment, whatever comes first. I don't think there's any set number of dates or weeks that makes it the right time, it's just how I feel about the person and our relationship. However, even leaving my profile up, I will stop paying attention to my messages after 3 or 4 dates, if I felt a really great connection. I wish this happened more often, lol.
With my last bf, after about 6 weeks of seeing each several times a week, I suggested we hide our profiles and we did. It was only a few weeks before I felt uninterested in checking my messages, and I was happily too busy seeing him to have time to put into meeting other guys anyway, but I waited to tell him. You know how you can think someone's great, then after a period of time, you start seeing more clearly and/or their true colors are revealed?
With the guy I was dating most recently, after about 4 dates I was interested enough to just focus on him, but I had some doubts (naturally, after 4 dates). So I was still checking messages now and then, a bit nervous that we'd "see" each other online, but we didn't in the 6 weeks that it lasted. I left my profile up the whole time as my doubts about him increased.
Oh, and don't delete your profile, hide it! Otherwise you have to start from scratch if this guy doesn't end up being for you.
Bottom line I think is doing what you feel comfortable with, but it doesn't mean you have to ask him to do the same thing at the same time.
ETA: Oh, and I would have felt anxious and a little hurt if I'd seen the ex online once we'd had a few dates, or even the guy I didn't end up being into, even though I wouldn't have been mad. I'd imagine they would feel the same way. But if this does happen, besides some uncomfortable feelings/awkwardness, it could lead to having a conversation about dating each other, which would probably be a good thing.