Take the two halves the word is built from. Feeble is weak, with no force behind it, like an arm that cannot hold the weight. Minded points at the mind. Put them together and you get a mind that cannot take the load: it gives way as soon as anything presses on it. English then aims that picture at two different targets. It can be aimed at a piece of thinking, which is the living use. It was once aimed at a person, and that is the old use the word is now remembered badly for.
From the word’s history
Wiktionary's tree gives feeble from Middle English feble, from Anglo-Norman feble, and minded from mind plus -ed. The compound is literally weak in the mind, which is still the picture underneath both senses.
Wiktionary 的構詞樹顯示：feeble 來自中古英語 feble，再上溯 Anglo-Norman feble；minded 是 mind 加 -ed。這個複合詞字面就是「心智虛弱」，這個畫面在兩個意思底下都還在。
Wiktionary, "feeble-minded"
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