My [30m] girlfriend [27f] thinks I'm gay, but I think she has commitment issues. It's complicated. How can I express that I want her as my partner?

TL;DR: Girlfriend of 9 months thinks I'm gay but I'm not. It's causing undue stress.

Long post, but I'm sure you get these every once in awhile. (names changed)

I'm 30, she's 27.

I love my girlfriend, Nancy. We've been together almost a year, and while that may not seem like a long time, I'm at a point in my life where I am looking to build a real relationship with someone. I am cutting my lease short to move in with her to an apartment which will add an extra 30 minutes to my commute, but I don't mind because the bus is comfortable (like a charter bus) and the apartment is beautiful. I love my job, my family, and I'm VERY much looking forward to moving in with her and building a relationship. My brother and his wife would live just down the road and they are amazing people. He's a natural leader who was leading people 30 years older than him when he turned 24, and she's a vice-president of a local bank. Community/family first, and just great, got-it-all-figured-out type of people. Love my brother beyond words.

It hasn't been easy: Before I met her, I had a friend named Sam who was a pity case. He was a recovering meth addict, and addiction counseling drop-out who was 1 semester away from graduating (unless he lied to me, which he might have been). His personality was very care-free and who-cares-what-anyone-thinks kind of attitude, I liked his shocking sense of humor, because I was trying to figure out who I was, and I had a social need of acceptance that he fulfilled. He filled his narrative with sob stories that, me having a huge heart, and a general need to help people, I fell for. We were friends for a few years, both musicians. In a very short time we became close friends. We would get fucked up and I would sleep on his air-mattress with him because I didn't want to sleep on the damn floor and I was too smart to drive drunk again. It was never physical. In fact, I'd already gotten my experimentation out of the way. I know I'm not gay or bi, through personal experience. He was just someone that I wanted to help, and it was refreshing to be around someone who was real, and not fake (or so I thought).

Anyway, his parents and his brother died within a very short time frame which, the big heart in me I just had to help him. I met my girlfriend during this time, who I became enamoured with straight away. I made a big boy decision to try to make a life with her, and I don't regret it at all. She's amazing, beautiful, motivated, and I love her flaws.

Fast forward, she thinks my relationship with Sam is inappropriate. I pitied him so much that I always cut for him, and tried to get her to see how he's not a bad person, but she suspects that, because of the nature of my relationship with him, that I might be gay. Huge misunderstanding. She's not used to the kind of street level gay-jokes that immature adolecents make. I tell her the truth: I experimented with a guy once (not sam) and realized then and there that I was most definitely straight.

Fast forward again: Sam comes out as gay, starts hanging out with two married gay dudes. Him being a friend of several years, when he invites us over, her and I go to a house party. Live music etc.. At one point, Sam asks me to give him a fake kiss in the window, kind of candidly. I assume it's because he thinks it would be funny, and I do the whole, two-thumbs-over-my-lips-pretend-to-kiss someone that I learned in grade school.

Nancy sees it and is devastated. This was a total oversight on my part, I should have realized that she would not think this joke was funny. She tells me how she feels, I apologize and reprimand Sam.

She breaks up with me right before she goes on a family trip to mexico. I can't focus at work, just flabbergasted that my sexuality is being questioned by the girl I love. She thinks my relationship with Sam went much further than it actually did, and is basing her assumptions on this, which I eventually make her see.

Fast forward again, after I try to defend Sam's character to her (at this point, I don't want to lose him as a friend) it turns out he lied to me about his family death, taking advantage of my big heart, after which I decide to cut him out of my life. I haven't talked to him since. Not just for Nancy, but because I'm grown and I don't need that kind of shit in my life. I realize how I was naieve and let a toxic person into my life. Fine. Gone.

Periodically, she'll see something she doesn't understand (pair of boxers I haven't worn in a year she thinks belong to someone else, or bottle of rum in the trash she thinks I had a frenzied homosexual party at my house about, all not true) and her mind immediately goes to "he must be gay and cheating on me with a guy"

Objectively, I am not feminine. I'm a tall skinny white male, yes, but I'm a 30 year old engineer and I've figured out who I am finally, and I'm comfortable with who I am. I most definitely prefer women, and with or without her, I will be fine. But she thinks I'm leading a double life and acting straight to cover up my gayness from my family.

The thing is, I have an amazing family, and no matter who I am they will always love me, and I know that. BUT I'M NOT GAY (or bi, as she has sometimes suggested).

Anyway... happened again last night. She saw some things out-of-place (I bought a different pack of cigs from what I normally smoke because the store was out of mine, and I kinda got drunk and slept in my swim trunks [yes, I drink more than I probably should] because I couldn't find my pajamas)

Now, she's going through a stressful period, finals for nursing school, having to move out of her small studio apartment, (she's always coming here because mine is bigger and more comfortable, which I LOVE when she's here) and I addressed what I believe to be the main issue:

She has cold feet, and isn't sure if she wants to finally commit to me. She admits that this is probably true. I don't care that this is STILL an issue, I forgive her faults (every time) because I'm not perfect myself, and I make mistakes, and I want her as my partner, so that in life we can both help eachother and grow and learn as a team. Not because I'm hiding my gay from my family. I have some good friends that are gay, I would not be ashamed if that were the case for me, because my family loves me no matter what.

It just seems like she can't get it out of her head that she thinks I'm gay or bi, and she has issues trusting me. Trust is supposed to be the foundation of the relationship, which I give her 100% but through a ridiculous series of misunderstandings, she cant seem to give me.

I know she loves me, which is why I think it's cold feet on taking the next step in our relationship.

I guess my question is, how can I encourage her to really trust me? I have never, not-one-time lied to her (except when I tricked her on a valentines day to surprise her) because honesty is part of my character, and I was hoping she would see that, but she still seems paranoid about the whole gay thing.

She apologized a few hours ago and said that she loves me, and that's ok, I'm not perfect either, but I just really want to put an end to this. It's like once every couple months the processes in her head rally against me, and no matter how loving and honest I am with her, the littlest thing can set her off.

She told me today that it's a spiral: she doubts me, then when she realizes she's wrong, she starts doubting herself.

What should I do? Does she really just want out of the relationship and wants me to break up with her? I am already committed.