Well technically humans are sexually mature during their teens, but that doesn't mean they are ready for breeding.

To each their own I guess, but 6 weeks seems really young for a mouse to start breeding. Males, maybe, but females I like to wait until they are at least 12 weeks old before breeding them.

She is one big girl that is for certain. I'm wondering if its a genetic thing since you say her relatives are big. Have you tried figuring out if it is genetic or if they are just really big eaters? If it is genetic, then send some of her offspring my way!