Words have both denotations and connotations. A denotation is a word’s literal meaning (or definition), and a connotation is a word’s implied meaning. With regard to connotations, words can be either positive or negative. It is possible to communicate the same thing using different words and have an underlying meaning be different. For instance, to say “My dog is fat” has a bit of negative connotation. But, to say “My dog is plump” has less negative and even positive connotation because of how (even though both sentences mean overweight) “plump” has almost a cuteness element to its tone.
Essentially, in this question, you're looking for the word that would be the least insulting. More broadly, when asked about positive connotation, you're looking for a word that is not viewed negatively.
Words like fat and cheap have negative connotations, especially when applied to people. Words like plump and frugal are much more positive.
