Even though Neelix struggles with Jealousy, some of it is coming from a good place. He wants to protect her from people like Tom who he feels would take advantage of Kes. And we learn in Elogium that he is not sleeping with her. He genuinely cares for her, and would risk his life to protect her.
From "Elogium"
NEELIX: Oh, no occasion. I just wanted to apologise.
KES: Apologise?
NEELIX: For the way I acted in the Mess hall. I was jealous.
KES: I know. I just wish you could trust me.
NEELIX: It has nothing to do with trusting you. It's him I don't trust. I've seen his kind before. They're all over the quadrant, as a matter of fact. They prey on naive, sheltered young women like you.
He also seeks advice on how to deal with his feelings-
From "Twisted"
NEELIX: Commander, I would imagine you've had some experience with women.
CHAKOTAY: Some.
NEELIX: Oh, come now. Ha! A handsome man like you. I bet women find you irresistible.
CHAKOTAY: Neelix, what's this about?
NEELIX: Er, er, er, have you, er, but have you ever been jealous?
CHAKOTAY: Of course.
NEELIX: You have?
CHAKOTAY: I imagine most people who've been in love have been jealous at one time or another.
NEELIX: I see. It's a perfectly normal response. Then why, why is it so unpleasant?
CHAKOTAY: Jealousy's about the fear of losing someone we love. There's no pain greater than that. Neelix, are you afraid you're going to lose Kes to someone?
NEELIX: No. I mean, I don't think so. At least I certainly hope not. I just can't seem to stop these awful feelings.
CHAKOTAY: Nothing makes us more vulnerable than when we love someone. We can be hurt very easily. But I've always believed that what you get when you love someone is greater than what you risk.
Neelix is a very emotive person. He doesn't hide his feelings. So where some other person might keep their feelings of vulnerability, worry, and jealousy hidden from their lover, that just isn't Neelix. He wears his heart on his sleeve(of his very hideously colored shirt). If we take this stuff about Neelix in context, and give him a fair chance, we see that these a very genuine and honest character development moments.
Conversely, with Tom Paris. Neelix has very good reasons for wanting to protect Kes from Tom Paris. He has a bad reputation aboard the ship, that Neelix has gotten wind of. He doesn't quite trust Paris.
But even Paris has a sympathetic angle here. He can't help that he's developed feelings of infatuation for Kes. He laments about it to Kim, but he knows he can't act on them, which he admits to Neelix.
From "Parturition"
PARIS: Oh, Harry. I'm in trouble.
KIM: What's new?
PARIS: I think I'm in love.
KIM: What's new?
PARIS: With Kes.
KIM: Kes!
PARIS: I know. I know. I never even saw it coming. I thought we were just good buddies. But there she was in my arms.
KIM: In your arms? Paris, you didn't.
PARIS: What? Oh, no. I didn't. I wouldn't. She stumbled during a flight simulation. I caught her. I held her for an instant. Are you going to play or not?
(Kim does a few notes.)
PARIS: A whole crew full of women and I have to fall for the one I can't have. Why do I do this to my self?
KIM: If you ask me, I say you enjoy it.
PARIS: Enjoy it?
KIM: Only thing that makes sense. You've been doing the same thing to yourself your whole life. Setting yourself up for rejection. You must enjoy playing the part.
PARIS: Hey, don't knock it if you haven't tried it. I just have to be more careful. I can't let myself be alone with her.
KIM: There's an old Chinese expression. Stay out of harm's way.
PARIS: That's not a Chinese expression.
And
PARIS: I, well, I guess the only way to say it is to say it. I am attracted to Kes.
NEELIX: Oh?
PARIS: To be honest, if you weren't around, I'd be knocking at her door. But I respect you, Neelix. And that's that. Everything you heard those guys saying about me, well, it was true. But it's not who I am anymore. At least not who I want to be. This upside down mission to the wrong side of the galaxy has given me a second chance, and I don't intend to blow it.
NEELIX: I see. Well, in a way I can't say I blame you. She is very attractive.
PARIS: She's devoted to you, you know.
NEELIX: Well, I did save her life. I'm sure she's grateful.
PARIS: Oh, she's a lot more than grateful. She loves you, Neelix. I wouldn't stand a chance. Nobody would.
NEELIX: There are others?
PARIS: If you ever doubt yourself, just look into her eyes. See the way she looks at you. You'll never doubt yourself again. And as far as I'm concerned, I'll just be her friend. I mean, if you don't mind.
NEELIX: I don't pick Kes's friends for her. Just my own.
More context, and here the situation is resolved. It's ironically Paris who really builds Neelix's confidence back up. And we see through his interactions, like this or the one with Chakotay, that he is not in any way remotely abusive, or potentially abusive. He's a warm caring guy who is both worried about Kes being abused by others, and feeling insecure by how beautiful she is compared to him. This is actually good honest stuff by Trek standards, concerning what might happen with relationships on a small ship where everyone is stuck together.
If anyone is interested in going back to see it in context, the episodes that deal with this are Elogium(during the cold open), Twisted, and Parturition, in that order.
Elogium and Twisted are actually 2 of the 3 final episodes of season 1(season 1 finale was supposed to be "The 37's", and Parturition was supposed to be the third episode of season 2.
