The word merry is descended from the Old English mirige or myrge meaning “pleasant”, “attractive”, “enjoyable”. This, in turn, was descended from Proto-Germanic *murguz meaning “short”, “brief”, “slow”, “leisurely”, in turn from Proto-Indo-European *mréǵʰus “short”, “brief” (via the oblique stem *mr̥gʰ-, the syllabic sonorants regularly became uC in Proto-Germanic). The shift in meaning from “short” to “enjoyable” seems to be through the concept of time seeming to pass quickly when one is enjoying oneself.
In Proto-Italic, this stem became *breɣʷis, which became Latin brevis, which retained the meaning of “short” or “brief”. The development /mr/ → /br/ was a form of dissimilation. I’m not sure if that was a regular development in Italic, or an irregular change (this same change, incidentally, also happened in Greek, whose cognate form in Ancient Greek is brakhús). There aren’t very many roots with the sequence /mr/, so it’s unclear. At any rate, brevis became Old French brief (Modern French bref), subsequently borrowed into English.