Have you consulted the theme description?
The size of the featured images is critical to display.
Are the images the correct size specified by the theme?
Theme description: http://theme.wordpress.com/themes/sight/
This theme has a featured post slider and that's what you see on the demo site ie. on the demo site no header image is being displayed.
Sight displays up to 30 of your latest sticky posts that have featured images in a prominent slider on the front page. To add a post to the slider, mark it as sticky http://en.support.wordpress.com/posts/post-visibility/#sticky-posts and give it a featured image.
Sight featured images
Large: 640 x 290 in the Sticky posts slider
Small: 290 x 290 thumbnails are used on the home, category, tag, archives, and search pages.
Setting a Featured Image http://en.support.wordpress.com/featured-images/#setting-a-featured-image
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