Greatly means to a very large degree. Greatly improved, greatly appreciated, greatly exaggerated.
It is formal and goes with past participles above all — greatly increased, greatly reduced, greatly missed. It is rare before an ordinary adjective, where very does the work, and that is what makes it sound written rather than spoken.
1adverbgreatlyTo a very large degree.
“Your help has been greatly appreciated.”
greatly is a degree.
Middle English
gretly
English, today
greatly
From Middle English gretly.
Etymology from Wiktionary, CC BY-SA