I have used a Sony A57 since they became available. I always have the resolution set for 16M and FINE for JPEGs. I just took an important set of photos that were intended for large blow-ups. But for some reason I cannot fathom, the images are all low resolution from 2-7 MB. What could be doing this? I can find no other setting that could reduce file size so drastically.
Based on the information you've given so far, I'm not yet convinced there is a problem.
Assuming you mean 2-7 MB (Megabytes), not KB (Kilobytes), that file size could be consistent with a full resolution JPEG. 2-7 KB would not actually fit an image, except maybe a tiny thumbnail or icon.
Look up the dimension of the image in pixels in your file browser - often by, for example, right-clicking and looking at image properties. Multiply the width by height to get number of pixels, and if it's near 16,000,000, you have a full resolution 16 megapixel image.
JPEG is a compressed format so the filesize does not correspond directly to the image resolution, but rather to it's content.
The JPEG algorithm achieves lower filesizes with images that contain less detail, so if you have areas with very little detail, such as out of focus backgrounds or blown out skies then that can lead to dramatically smaller filesizes, however there's nothing to worry about because you are not losing any resolution.