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Definition of mightily : 1. In a mighty manner; with might; with great earnestness; vigorously; powerfully.
2. To a great degree; very much.

Synonyms:

correctly, right on, flop, powerful, in good order, justly, the right way, properly, mighty, right, aright, decent, decently

energetically, ardently, potently, forcefully, snappily, powerfully, vivaciously, spiritedly, effervescently, fervidly, strongly, zealously, actively, forcibly, vigorously

huskily, firmly, toughly, robustly, sturdily, stably, formidably, stoutly, muscularly, brawnily, vitally

commandingly, authoritatively, masterfully, competently

Usage examples:

• As there is no mystery in this matter, it may as well be stated here that young Heaton ultimately returned to England, as drowned men have ever been in the habit of doing, when their return will mightily inconvenience innocent persons who have taken their places. - "Revenge!", by Robert Barr.
• Roger said something, that night, that interested me mightily. - "Dawson Black: Retail Merchant", Harold Whitehead.
• I got mightily interested in coal. - "The Boy With the U.S. Miners", Francis Rolt-Wheeler.