I was wondering why in this sentence
I can enlist her support for follow up in my weekly meeting tomorrow
“follow up” was used instead of “following up”?
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Follow up has been used since the early twentieth century as a noun, the act of "following up".
In case a reply is received to a letter marked for follow-up, before the follow-up date arrives, the file clerk knows that a tickler has been made when she sees the date notation in the upper right hand corner of the filed letter. —American Gas Engineering Journal, 1926
(A 'tickler' in office contexts means a formal reminder of something to be done in the future: it 'tickles' the reader's memory.)
Note that the phrase is employed both as the nominal object of the preposition for and as an attributive nominal modifying date.
Note, too, that the phrase is written here with a hyphen, follow-up, to signal that this is not an ordinary verbal use. This sort of hyphenation is falling out of use, but I recommend it as a valuable courtesy to the reader.