Rightly
Part of speech: adverb
Definition: Aright, in a right manner.
Example sentence: Britain rightly sees herself as a global good citizen, but she must reconcile ambition with power, ends with means - shedding utopian idealism in favour of a more rugged internationalism, putting the national interest first, not last.
Justly
Part of speech: adverb
Definition: In a just or fair manner; of great justice.
Example sentence: Laws are to be enforced justly but firmly, with an iron hand. This is the case anywhere, even in a family.