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puff someone or something up
to boost or promote someone or something. Judy puffed Nell up so much that Nell could not begin to live up to her reputation. Don't puff up your own accomplishments so much.
to swell up. Her finger puffed up and she thought she might have an infection. His eyelids had puffed up during the night.
puff up (into something)
to assume a larger shape by filling up with air or water; to swell up into something. The strange-looking fish puffed up into a round ball. The fish puffed up and stuck out its spines.