In my post on shevach, I mentioned the Yiddish word shvach, which derives from the German schwach, meaning "weak". Since German and English are related languages, I tried to find an English cognate to the German. The closest thing I found was the obscure Scottish word "swack", mentioned here:
Swack, to deal a heavy blow; akin to the vulgar English whack, to beat severely; a swashing blow, a heavy blow; etymology uncertain. The Teutonic schwach, has an opposite meaning, though there may be some connection of idea between a heavy blow and a blow that weakens him on whom it falls.A parallel term in English would be "beat" - meaning both "to strike" (as a verb), and "worn out, tired" (as an adjective.)
Hebrew might also have an example. The root חשל appears once in the Bible (Devarim 25:18), where it means "weakened, lagging":
אֲשֶׁר קָרְךָ בַּדֶּרֶךְ, וַיְזַנֵּב בְּךָ כָּל-הַנֶּחֱשָׁלִים אַחֲרֶיךָ--וְאַתָּה, עָיֵף וְיָגֵעַ
"When they encountered you on the way, and you were tired and exhausted, they cut off those lagging (hanecheshalim) to your rear"
Tigay, in the JPS Devarim writes (note 57):
Medieval Hebrew grammarians took the term to mean either "broken", based on Aramaic h-sh-l, "crush" (the verb is now known in Akkadian, too)
This is the view of Steinberg as well. Interestingly, from this sense of חשל we get the opposite of weak. Klein writes that the Aramaic and Akkadian "to crush" led to Hebrew "to forge, hammer, shape, mold", which in Modern Hebrew became "to strengthen".
However, Tigay continues:
or "weakened", taking the root h-sh-l חשל as a metathesized form of h-l-sh חלש, "be weak"
This is the view of Ibn Ezra, as well as Klein, who does not connect the two senses of חשל at all.
An additional theory is proposed in a footnote to the Ibn Ezra in the Torat Chaim edition by Asher Weiser, that נחשל could be related to נכשל / כשל - "stumble, fail, be weak (see Tehillim 31:11)". Kaddari quotes this view as well.
So again, we have what appears to be one root - חשל - with opposite meanings - weak and strong. But a careful examination of the development of the meanings shows that this isn't some unusual phenomenon in Hebrew where words take on opposite meanings, but rather an understandable evolution of meaning that appears in many languages.