Visibly means in a way anybody could see. The feeling did not stay inside.
It attaches to states rather than actions, giving visibly shaken, visibly upset, visibly relieved, and each means the emotion showed on the outside. That is its whole job in reporting, since a witness described as visibly distressed is being described from outside rather than interpreted. It also works plainly, so something visibly worn has obvious wear. The adjective visible and the noun visibility belong with it.
1adverbvisiblyIn a way that can plainly be seen.
“He was visibly relieved when the call ended.”
Proto-Indo-European
*weyd-
Latin
visibilis — that may be seen
Old French
visible
Middle English
visible
English
visible
English, today
visibly
From visible + -ly. visible comes from Middle English visible, from Old French visible, from Latin visibilis (“that may be seen”), from Latin videre (“to see”), past participle visus; see vision. Displaced native ġesewenlīċ.
Etymology from Wiktionary, CC BY-SA