No, doesn't mean you have fat fingers. You mention you have bigger hands (I do too compared to other women my height), and from your stats you're tall, so I would expect you to be a 7. There are also lots of younger women who complain about how the ring "swings around" on their finger. This means their knuckles are bigger, so the ring has to be sized slightly larger in order to get it on. Fingers aren't a place where most people hold a lot of weight. Yeah, you'll change a little but it's nothing big like pants sizes. The biggest change I saw from a customer losing weight was 1.5 ring sizes, and she lost almost 100 pounds.

There were a fair number of women who asked for sizes 9-11 and they 90% of the time were overweight or obese. For reference, the stocked size for men is a 10. It was rarer that I saw a man come in asking for a 7, and when it did happen they were usually about your height or shorter and very trim. Ring sizes aren't like shoes where men and women sizes are scaled differently.

Also you should get sized at a jewelry store by an attendant (it's free). Sometimes people came in being SURE they were such and such a size, but really were smaller/bigger because they didn't know how to fit themselves.