Well, I was awake last night, thinking of my impending doom at the hands of an Epic that's powers are cereal based, when I started thinking, 'Hey, what makes an Epic an Epic, and what is it in their past that specifies their power portfolio? And how can I get potato powers to enslave the Irish?' Well I believe the answer is partially stated in the books, but certainly not outright stated.
•We have evidence to believe Calamity is an Epic, yet we have nearly no idea what his power portfolio is. There is the always the option that he is a high Gifter, but it's not certain yet.
•The Reckoners and Lorist have figured and speculated that something in an Epic's past is what creates there weakness, example; Sourcefield and KoolAid, poisoned as a child with KoolAid. Steelheart and Men Who Don't Fear Him, Steelheart was a school bully, yet it is unknown if someone who didn't fear him almost killed him.
•We can assume some near-death experiences happened to Nightweilder with sunlight, Megan with fire, and Newton with her faimly (she is weakened by compliments and afraid of not being as good as her faimly)
•From what is stated in the books, ONLY WEAKNESSES are specified by an Epic's past (or so from what we know)
My conclusion is that only an Epic's WEAKNESS is specified by their past, and their powers (from what we know and can theorize) are completely random.
P.s. They never did find out Regalia's power, yet when David killed her, he proved she was not a High Epic, she had no powerful protective powers. Prof's history and near death experience is unknown, only that he was a schoolteacher, dated Tia, and was friends with 3 other Epics, so we really can't determine what Prof's weakness is without knowing more of his history. (However there were small blurbs about how Prof disliked contest.)
~Stay Duckie My Friends!