Many website building platforms allow to insert the caption for images. However, they all will be in a simple style as a small text below the image. If you want to showcase the image caption with different styles, here are the widgets for you. There are four styles of widgets to show image caption and you can get the instructions for Weebly site here.
Image Caption - Slide Down Style
Slide down caption. Link possible.
Image Caption - Horizontal Split Style
Horizontl Split Style Caption.
Image Caption - Vertical Split Style
Vertical Split Style Caption
Image Caption - Slide Up Style
Image Slide Up Caption