deservedly

(degree, manner) In a way or to a degree that is deserved or merited.

1847-48, William Makepeace Thackeray, Vanity Fair, 2008, Digireads.com Publishing, page 437, Emmy, he remembered, was at one time cruelly and deservedly jealous of Rebecca, […] .

1986, Facts on File, Editorials on File, Volume 17, Part 2, Infobase Publishing, page 949, The vote for Scalia was unanimous, and deservedly so.