fat rat
fat rat
fat rat
Fat rat is probably the phrase you are looking for. A rat is a rodent, and fat means overweight.
Using rhyming word pairs to create synonyms of other descriptive pairs is often used as brain teasers for children. For example, an overweight referee is also a plump ump.
Rhyming word pair for home for a rodent?
Rhyming word pair for happy boy?
Mouse house
Fatcat!
pink mink
fat rat
pink mink