There is no "generally accepted definition" of what is the normal body weight of a mouse. The closest might be "the body weight of a mouse fed standard laboratory chow" but which mouse strain and which chow? And which age and sex? Obesity is usually defined as a statistically significant increase in the amount of adipose tissue above that of controls, but this depends on what are the controls, statistical power, and how the amount of adipose tissue is measured.
If you want some numbers, for "normal body weight" of individually-housed C57BL/6J male mice at about 20 weeks of age fed Teklad 8601 chow, the percentage of body fat measured by MRI is about 8-10% of carcass weight. Body fat as a percentage of carcass weight corresponds very roughly with human BMI, so a mouse with 10% body fat is equivalent to a male human athlete, a mouse with 25% fat is observably chubby to the untrained eye, and one with 50% fat is morbidly obese.
This takes into account age and sex. They also have charts for other strains.
In terms of obesity, I would just look for significant increases in BW and adiposity (adipose tissue mass, we normally look at epididymal fat pad mass), although the best method would be with CT or MRI for whole body adiposity.
Like with humans, there may be a spectrum (ex. underweight, normal, overweight, obese, morbidly obese). However, I doubt this exists because I don't think we know (or care to know) what a "normal" or "healthy" level of adiposity is in mice.
I think what's important is how your values compare to control mice, like when feeding chow vs HFD in my previous answer.