If the girl is more concerned about the size of the ring then she is with spending her time with you, then she’s the wrong girl.
My wife wanted a smaller ring for several reasons, I spent less then $2k almost 15 years ago. We both had custom wedding rings made and hers was less then mine. Since then I’ve bought her nice earrings and a necklace but she only wears them on rare occasions when we go out.
Edit. Both of our wedding rings and her engagement ring combined were less then a new stern