The tendency of human psychology for anthropomorphism (attribution of human traits, emotions, and intentions to non-human entities ) is reflected in literature through the use of the 'personification ' device.
But are we really trying to personify fat when it is cited as stubborn by the OP ? or is it the case of only using a human motif. Mere employment of human imagery does not constitute personification.
Is it( ever) 'The rebellious hair refusing to come to order', 'The stubborn fat has apparently decided not to budge' For personification - regardless to the extent or the trait considered - it is essential for the entity concerned - to be invested with a human ego.
*In literature, allusions are used to link concepts that the reader already has knowledge of, with concepts discussed in the story^ (Wikipedia)
My answer is as under
an expression designed to call something to mind without mentioning it explicitly; an indirect or passing reference.
"an allusion to Shakespeare"
synonyms: reference to, mention of, comment on, remark about, citation of, quotation of, hint at, intimation of, suggestion of; implication, insinuation
"the bird's name is doubtless an allusion to its raucous call"
the practice of making allusions.