1630s, "in a hopeful manner, with grounds of expectation for success," from hopeful + -ly (2). As a replacement for the admittedly awkward it is to be hoped that, attested from 1932 but avoided by careful writers.
we searched hopefully for a good position
hopefully the weather will be fine on Sunday
Hooverville
hooya
hop
hope
hopeful
hopefully
hopeless
hop-head
Hopi
hoping
hoplite