1) Accurately 2) As deserved 3) Deservedly 4) Honestly 5) In a just manner 6) In an honorable manner 7) In conformity to fact or rule 8) In fairness 9) Justifiedly 10) Rightly 11) With good cause 12) With honesty 13) Without bias 1) Byright 2) Deservedly 3) Fairly 4) Justifiedly 5) Morally 6) Rightly 7) Truthfully 8) Virtuously 
• (a.) In a just manner; in conformity to law, justice, or propriety; by right; honestly; fairly; accurately.
Just'ly adverb [ From Just , adjective ] In a just manner; in conformity to law, justice, or propriety; by right; honestly; fairly; accurately. 'In equal balance justly weighed.' Shak. « Nothing can justly be despised that can not justly
[adv] - in accordance with moral or social standards
adverb in accordance with moral or social standards; `that serves him right`; `do right by him`
in a just manner; honestly; fairly: Deal justly with the prisoners. · in conformity to fact or rule; accurately. · deservedly; as deserved.