"You'll fit right in" isn't necessarily about his size…
Fitting denotes adopting to the end in view, the use proposed, or the work to be done; fitting takes place when the expected end result is defined and known: people fit clothes to the body, eat food fit for a king, and wear shoes that fit their feet. Fitting denotes the undertaking of making a thing fit something else.
"Suiting" makes a thing suitable, agreeable, or in line with one's expectations or standards otherwise established. Whatever suits agrees with one's ideas or feelings. "Suit yourself" is a good example. Suiting implies being in the order a thing ought to be.
Matching means finding a mate; two things are mates when they correspond to each other, perhaps equal or rival each other.