My (27m) significant other (28f) is recently started taking the pill and prefers that I not use condoms. I'm not sure I'm comfortable with that. Am I being unreasonable?

I've been with her for two years, and up till a few weeks ago she had an IUD. It has now been removed and she's on the pill. Even though I know that the pill is pretty reliable, I DO NOT want a child, and therefore want to use condoms as well just as a backup method. I'm especially worried since my girlfriend is obese. I asked her if she would be willing to have an abortion if pregnancy did occur, and she said he wasn't sure.

I do not want a child right now (MAYBE in a few years), and I cannot help but think that my girlfriend would not be entirely disappointed if pregnancy did happen. She's made it clear that she wants more children in the future and has said that if she got pregnant we would "deal". This makes me even more uncomfortable. To make matters worse, the last time we used a condom it got stuck inside of her (which was incredibly unpleasant for her). This made me think that maybe I'm bringing some unpleasantness to this relationship over nothing. Am I overreacting here?

tl;dr My girlfriend wants me to stop using condoms, and I don't know if I am comfortable with that.

Edit: Added tl;dr.