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?
house mouse
pink mink
fat rat
fat rat
plump ump
mouse house, rat flat
Mouse House or 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.
Rhyming word pair for Friend who does not arrive on time?