I had the same problem and seems like we haven't had an accurate solution. Hope this can help other people.
After take time exploring around, I finally found the answer. This is my code to get file attach with jQuery:
var attach_id = "id_of_attachment_file";
var size = $('#'+attach_id)[0].files[0].size;
alert(size);
This is just the example code for getting the file size. If you want do other stuffs, feel free to change the code to satisfy your needs.