with.
理由：句子含義：他哥哥吃得太多,鍛煉太少,所以很胖.這里his brother is so fat句子成分已經完整,所以后面部分只能是狀語了,with too much food and little exercise 是介詞短語做原因狀語.補充一下：（）里只能填because of或 because那么就填because of 了，這里填with也是可以的，都是介詞短語表原因。because是連詞，所以后面要加從句，而because of 是介詞，所以后面加短語，too much food and little exerise就是短語啊，我們可以改成，because he has too much food and too little exerise. 你看，后面加上he has就成句子了，所以就用because 了。