너무 is "too" like "this is too salty." 많다 is "to be many". like "there are many people. Here they work together by adding "too" + "many". 사람이 많아. - There are many people. 사람이 너무 많다 - There are too many people.
너무 means too/too much and 많이 means a lot/much. If you said 많이 운동하지 마십시요, it would be more along the lines of "Don't exercise a lot". But adding 너무 emphasizes that the speaker doesn't want you to exercise "too much" or to overdo it.