"Not as heavy as an elephant." Which literary device is this?

Solution 1:

Yes, your friend used hyperbole:

Hyperbole, derived from a Greek word meaning “over-casting” is a figure of speech, which involves an exaggeration of ideas for the sake of emphasis. It is a device that we employ in our day-to-day speech. ...[H]yperbole is an unreal exaggeration to emphasize the real situation. Examples:

• Your suitcase weighs a ton!
• She is as heavy as an elephant!
• I am dying of shame.

Poets use hyperbole as well, as in this passage from Romeo and Juliet:

The brightness of her cheek would shame those stars,
As daylight doth a lamp; her eyes in heaven
Would through the airy region stream so bright
That birds would sing and think it were not night.

There is a type of hyperbole called auxesis, meaning growth, increase:

a form of hyperbole that intentionally overstates something or implies that it is greater in significance or size than it really is.

The "growth/increase comes in with serial exaggerations:

Arranging words or clauses in a sequence of increasing force. In this sense, auxesis is comparable to climax and has sometimes been called incrementum.^[2]

A familiar example is the statement at the beginning of The Adventures of Superman:

"Look! Up in the sky! It's a bird... it's a plane... it's Superman!"

Each element builds up to greater and greater significance.

Your friend starts by asked you to help him pick up a desktop printer (mild hyperbole). You asked him if two men were needed (you payed a part in this) to which his answer was at least an implied positive. Th then said, Have you ever seen an adult elephant? Well, it (the printer) is not quite as heavy as that.

Auxesis is used in humor as well as in serial exaggeration and poetry.

I think this might be the type of hyperbole used here.

_{[1] Literary Devices
[2] Silva Rhetoricae}

Solution 2:

This type of ironic understatement is known as litotes.

Google defines litotes as:

Ironical understatement in which an affirmative is expressed by the negative of its contrary (e.g., you won't be sorry, meaning you'll be glad ).