The behavior you're describing occurs because of the thumbnail settings in phpBB. If the image is within the maximum dimensions set for thumbnails, or if thumbnails aren't enabled, then the image is displayed as-is. ("very large, and cannot make it bigger")
When enabled, if the image is taller or wider than the maximum thumbnail setting, or is taller or wider than 400px if no other maximum has been set, then a thumbnail image is generated and that is what you first see when viewing the attachment. Clicking on the image then shows the full non-thumbnail version of the image. (The behavior you're seeing here on phpBB.com/community.)
The behavior you're describing on your board sounds most likely that thumbnail generation is simply disabled. Or if it is enabled, then the "Maximum thumbnail width/height in pixel" in the phpBB ACP Attachment Settings must be larger than you really want it to be.