with.
理由：句子含义：他哥哥吃得太多,锻炼太少,所以很胖.这里his brother is so fat句子成分已经完整,所以后面部分只能是状语了,with too much food and little exercise 是介词短语做原因状语.补充一下：（）里只能填because of或 because那么就填because of 了，这里填with也是可以的，都是介词短语表原因。because是连词，所以后面要加从句，而because of 是介词，所以后面加短语，too much food and little exerise就是短语啊，我们可以改成，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。