Why should I use JavaScript Library if it may effect the performance of a web site?

This is an important question and I can not decide when and why should I use JQuery or another JS Library.

Is is very easy to add JQuery to the project and write short commands. It saves me time to write much code in JS that someone already wrote it for me and checked it is working in all browers.

But cellular or mobile programming is not like that. Each additional file directly affects the performance. My testing with JQuery mobile damaged performence badly due to file size, 17KB.

So the question is whether or not it better to spend a little time to write my own JS suitable for what I need and not working with files ready? When is it better and when it is really not?

Be glad to hear your opinions.