She's beautiful. I love Rottie's. They're pretty awesome dogs. Very into their people. They are leaners. Give them a good scratching and they'll love you forever pretty much. They a herding breed/working breed. Pretty versatile dogs when in the right hands. I don't know of any breeders who breed for more than looks anymore but I imagine they can still be found overseas pretty readily.
You say she doesn't eat much. If memory serves, rottie's are prone to thyroid problems so besides inactivity, thyroid could attribute to her being overweight. Example, Shasta, though GSD, is really lazy. She's my couch potato. Content with the short walk down to the mailbox and back. She gains weight pretty easily from inactivity and 2 cups a day. I watch her weight closely and if she starts looking a little chunky, she gets dropped to a cup a day split between her morning meal and her evening meal. Within a few days to a week, she's got her girlish figure back which is saying something because she's a pretty stocky girl. If she didn't drop the weight with the food intake change and slight increase in activity (against her will lol), she'd be checked out for possible causes as to her weight issues.
Give it a few weeks of the runs and keep an eye on her physique. Bear in mind, rottie's have more of a barrel shape to them but should have some tuck when in good bodily condition.
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Shasta GSD 5/5/10 CGC, ITD, TC
"Dax" Thor z vom Weberhaus CAX, CGC, ETD, HCT, RATI, RATN, TC 3/18/2013
Zena GSD 6/1/03-2/16/2016
Riley GSD/BC 1/10/05-2/1/2013