Think of a string attached to your heart. If it is tugged slightly, you feel something.

to cause strong feelings of affection or sympathy He looked into his son's smiling eyes and felt a tug on his heartstrings. f something tugs at the heartstrings, it makes you feel sad or sympathetic towards it.

give you my heart on a string means that you will give them full possesion of your heart you are pretty much telling them that they own your heart and they have the ability to do what they please with it the string meaning control and interpreted as so.(http://answers.yahoo.com/question/index?qid=20081125153932AAPTDN2). This term means to really get to you emotionally deepest feelings or affections Origin: orig. tendons or nerves formerly believed to brace the heart http://www.yourdictionary.com/heartstrings

If something tugs at the heartstrings, it makes you feel sad or sympathetic towards it.

هده عبارة تعني أن شيئا يحرك المشاعر