Strongly means with great force or firmness of feeling. Strongly agree, strongly advise, strongly built.
It attaches to opinion verbs above all — strongly believe, strongly deny, strongly recommend — and it is the standard top and bottom of a survey scale. Note that strongly is about degree of conviction, where firmly is about steadiness.
1adverbstronglyWith great force or firmness of feeling.
“I strongly advise you to see a doctor about that cough.”
strongly is a degree.
Old English stranglice is strong plus the -lice ending that makes adverbs.
Old English
stranglīċe — strongly
Middle English
strongliche
English, today
strongly
From Middle English strongliche, strangliche, from Old English stranglīċe (“strongly”), equivalent to strong + -ly.
Etymology from Wiktionary, CC BY-SA