Fat Rat.
fat rat
Fat rat is probably the phrase you are looking for. A rat is a rodent, and fat means overweight.
Rhyming word pair for home for a rodent?
Rhyming word pair for happy boy?
pink mink
fat rat
fat rat
plump ump
mouse house, rat flat
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.
stout trout, overweight skate