From BiblePortal Wikipedia

King James Dictionary [1]

Deeply, adv.

1. At or to a great depth far below the surface as a passion deeply rooted in our nature precepts deeply engraven on the heart. 2. Profoundly thoroughly as deeply skilled in ethics or anatomy. 3. To or from the inmost recesses of the heart eith great sorrow most feelingly.

He sighed deeply in his spirit.  Mark 8

He was deeply affected at the sight.

4. To a great degree as, he has deeply offended.

They have deeply corrupted themselves.  Hosea 9

5. With a dark hye, or strong color as a deeply red liquor deeply colored. 6. Gravely as a deeply toned instrument. 7. With profound skill with art or intricacy as a deeply laid plot or intrigue.

This word cannot easily be defined in all its various applications. In general it gives emphasis or intensity to the word which it qualifies.

Webster's Dictionary [2]

(1): ( adv.) Very; with a tendency to darkness of color.

(2): ( adv.) Profoundly; thoroughly; not superficially; in a high degree; intensely; as, deeply skilled in ethics.

(3): ( adv.) At or to a great depth; far below the surface; as, to sink deeply.

(4): ( adv.) With profound skill; with art or intricacy; as, a deeply laid plot or intrigue.

(5): ( adv.) Gravely; with low or deep tone; as, a deeply toned instrument.