I've dated insecure girls before. I think you have two best plays in your playbook. They feel slightly contradictory, but resolving that paradox is part of your job.
1) Do not cater to her insecurity. If she asks you once a week whether you're cheating on her, are going to cheat on her, would rather be with other woment, etc., she's just begging you to validate her. You don't have to be hard on her, but occasionally, telling her that it hurts your feelings that she doubts you so much may be in order. Is it possible that this will cause problems or even end the relationship? Yes. It absolutely could. The problem with an insecure girl, though, is that she's not being honest with you. She's not even being honest with herself. The last insecure girl I dated made it so far as to accept a marriage proposal from me before she realized, "Oh, wait. I'm not actually all that attracted to or interested in this guy."
2) Build her up. Don't just help her to feel good about herself for a little while but sincerely help her to become more confident, trusting, and self-aware. This is going to be hard work and in the end, the confident woman you've helped to create might realize that you were validation, not true love. It's worth the risk for two reasons. One, if it IS true love, then you'll have earned a wonderful partner. Two, you will ultimately find the affection of an insecure woman to be both stifling and unsatisfying.