Correct spelling, explanation: visibly comes from the same word family as visible or vision and all the words derive from Latin. More precisely, the original form of visibly is videre, which could be translated as to see. The word also appeared in Old French and then in the Middle Ages visibly entered English too. Today visibly is a widely used adverb.

Definition of visibly:
1. adverb – something which is clearly seen or understood, something obvious,
She was visibly disappointed when I told her that she was not chosen for the project.

Expressions with visibly:
A few popular expressions with visibly are: visibly surprised, visibly different, and visibly touched.
Kate was visibly surprised when Tom asked her to marry him, but she said yes at once.
It is true that both dresses are in the same style, but they are visibly different and I definitely prefer the red one.
The audience was visibly touched when they were leaving the theatre after the play had finished.

Incorrect spelling, explanation: one of the most popular endings of adjectives in English is -able, which changes to -ably when an adjective becomes an adverb. Therefore, the spelling of visibly is quite unusual and because of that, a number of English speakers spell it as visably. This form, however, is wrong as there is an -i letter in the last syllable instead of an -a and the only correct spelling is visibly.