At the Olympics (at least the winter version), some events begin at the peak of a mountain. All Olympic events are so competitive an athlete needs to deliver a peak performance in order to win a medal. A few of the athletes — and some of the fans — have a hairline featuring a widow’s peak at the top of their forehead. All of these peaks seem pretty closely related. But then again, any atheletes who catch the flu at the Olympic Village might end up looking peaked. That last one is generally pronounced “peek-id” in the US, probably because people wanted to make it clear that it wasn’t the same word.
Except that it is the same word. “Peak” is a derivation of the earlier word “pike.” Peak appeared in the 1500s. A pike was a spear, and the word also meant the pointed tip of the spear. When “peak” came along it was used for all sorts of things that had sharp points; the top of a roof, the pointed top of a craggy mountain, and so on. The figurative usage of “peak,” where it refers to the highest point of success or achievement or intensity is an easy jump from the idea of a physical peak.
The adjective form of “peak,” which is “peaked,” appeared about the same time as the noun and was — and still is — mostly used in the same sense. In most of those senses it’s pronounced as you’d expect: “peek’d” rather than “peek-id.” A “peaked roof” is just a roof with a peak. It wasn’t until the 1800s that another meaning arose, apparently in casual usage in England. People noticed that when you were ill or malnourished you got thinner, which made some of your features look more bony and “pointy.” Remember that “peak” came from “pike,” and was still associated with sharp points, so “peaked” came into use to mean “I can tell from your pointy features that you’re not well.”
As most English words coined in England do, “peak” and “peaked” spread to the US, still in the 1800s, and pretty much kept all of those original meanings. The only difference was that for some reason English speakers in the US are sometimes more finicky and precious than their counterparts in the country where the language actually came from. Compare, for example, how US speakers pronounce “lingerie” as the pseudo-French “lawn-je-ray,” while in England the same word is pronounced the way it looks: “lin-je-ree.” The US speakers evidently thought they needed to differentiate between the “peaked as in roof” and “peaked as in malnourished,” the malnourished version acquired an extra syllable, which it still has. And that gives us the current situation: somebody thought it was a different word so they changed the pronunciation, that caught on, and now the pronunciation is different so lots of people think it’s a different word. Figures, doesn’t it?
Incidentally, “finicky,” which I used a few sentences back, means “excessively picky.” It showed up around the early 1800s. “Finicky” is based on the word “finical,” which meant about the same thing and appeared around three centuries earlier. Some think that its original root might be “fine”, as in “you’re making too fine an argument” (an expression that means your argument is too particular, not that you’re in peak argumentation form).