This is the 8002nd most frequent Japanese word.
太ら
"太ら" is the stem form of the verb "太る," which means "to gain weight" or "to become fat" in English.
The usage "太りすぎて" combines "太り" with "すぎる" to indicate excessiveness in gaining weight.
彼は太りすぎて、健康を心配しています。
He is worried about his health because he has gained too much weight.
In this case, "太らない" is the negative form of "太る," expressing the intention of not gaining weight.
太らないように注意しています。
I am cautious to avoid gaining weight.
The word "太り" (ふとり) refers to gaining weight or becoming fat in this sentence. It is used as the verb stem of "太る".