Brindle mice (to varying degrees) have an obesity gene that is really the same gene, it just means that they are obese. They did studies and found that even when a mouse is kept on a very strict diet, the proportion of body fat to other body ingredients remain constant... so if you put them on a diet they lose a certain amount of fat and a proportionate amount of muscle tissue. It's very unhealthy, actually, to keep an obese mouse on a diet. Poor things. I've had some VERY fat mice, but it is variable and the fattest ones don't tend to breed well and the thinner ones breed for longer periods of time, so I haven't had many mice get severely obese in my colonies for a long time, even though I have a lot of yellow mice.
And yes, those mice are great! Just love em!