alt attributes don't help with web searches. They are for accessibility. In other words, alt text is read aloud by screen readers & it appears in browsers when images fail to load. My advice is to use alt attributes on the thumbnails the same way you do with other images. To add meaningful text to your full-size images, use the title attribute. See example below:
<a class="fancybox" data-fancybox-group="gallery" href="http://placehold.it/400x320.jpg" title="Full Size Image Caption"><img src="http://placehold.it/160x120.jpg" alt="thumbnail1" /></a>
Nancy O.