Adding an image overlay?

For a website I’m working on, the clients want any large images in post content to link to an attachment page with the full sized image. To indicate that there’s a larger image if the smaller image is clicked on, they want a small magnifying glass image overlay to display over the image. Obviously this needs to not appear on images which don’t have a bigger file to click through to.

I’ve tried messing around with what’s there with CSS, but I really need another element to work with and put the overlay in. I understand that to do this I need to write a filter(?) that will work when a linked image is in the content, but I’m new to that side of things and really have no idea where to start.

Could someone point me in the right direction? Or is there a plugin that does something similar?