This is something that makes you uncomfortable, and I don't think anyone should tolerate anything that makes them uncomfortable in a relationship. Having said that, you do seem very insecure. In your OP you say that it makes you feel ugly. This feels like an odd response to me. If I felt my partner was checking someone out, I might find it disrespectful, I might feel pissed off, but it wouldn't make me feel ugly.
Your self esteem seems to depend too heavily on how your partner feels about you. You also seem to be under the impression that he can only be attracted to one person, and if he's checking a girl out, he's no longer attracted to you because he's now attracted to her. Of course attraction doesn't work that way.
As for wanting to be the only person he wants to be with, the reality is there are always multiple people out there for us. I'm sorry to say there's no such thing as soulmates, true love, the one, etc. Belief in these concepts results in placing too high expectations on a relationship.
People in relationships will sometimes be attracted to other people. They may even sometimes develop little crushes, but they ultimately stay with their partner and don't act on it because they choose their partner. I'm not condoning your partner ogling other women, but also you have to realise that him being attracted to other women doesn't detract from the fact that he's choosing to be with you.