From JGram: ～う／ようものなら： もし～ようなことをしたら．．．（大変なことになる） Once if (one) happen to ... , then (bad consequence)."
So the first part of the sentence does not imply the listener is the subject, but the 'that person' in the next part of the sentence instead.
So basically it is saying: "You should be careful because if you help that guy out once, he will take advantage of that (act) and ask for favors very often."