Rightfully

Adverb

 * 1) In accordance with what is right or just; fairly.
 * 2) *The only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others. His own good, either physical or moral, is not sufficient warrant. -- John Stuart Mill
 * 3) Rightly, correctly.
 * 4) *1590, Edmund Spenser, The Faerie Queene, II.viii:
 * Ne euer will it breake, ne euer bend. / Wherefore Morddure it rightfully is hight.

Thesaurus
appropriately, as is proper, as is right, by right, by rights, condignly, correctly, deservedly, disinterestedly, dispassionately, duly, equally, equitably, evenly, fair, fairly, fittingly, impartially, impersonally, in all conscience, in reason, inequity, injustice, justifiably, justifiedly, justly, meetly, properly, right, rightly, upon even terms, warrantably, warrantedly, without distinction