Does Mac OS X v10.8.5's Preview have a compression option for JP(E)G images?

Jpegs are pretty much already compressed, so there is no such option.

That's not all that large. Perhaps you should scale it's depth using a photo editor such as GraphicConverter 9.5. Or maybe that is just due to the size of the image. You can also rescale the size. GC is an excellent tool for manipulating image files. But compressing them won't accomplish much if anything. JPEG is a compressed format.

There are various levels of JPEG compression. In Photoshop, they're defined as the maximum compression of 0 (please completely destroy me) to minimal compression of 12 (preserve as much detail as possible). Sizes naturally go from tiny (zero) to larger (12) as more or less overall compression is applied.

How you would change it in Preview, I don't know as I use Photoshop for all image work.

What a person is used to I suppose, but to me, 3 MB is teeny tiny. Normal file sizes I routinely work on range from 20 MB to 750 MB and some over a GB, with 120 MB images being the most common.

Always make and work with a copy of your original image.

.jpg is a 'lossy' compression, so once saved to a smaller file size, the detail cannot be regained by attempting to re-save the smaller image back to a larger file size.

In OS X 10.8.5, using Finder, I used File Export (but you can also use Save As, revealed with Command+Duplicate in the Finder menu)

The original digital image was 6.7MB, created with a digital camera at 4000 pixels wide x 3000 pixels height.

Using the slider as shown above to change the Quality setting in increments of 2 'bars' here are the file size results.

Example image saved at '2' quality (smallest file size): {click on the images to enlarge on your screen}

A very 'busy' scene, saved at the smallest file size, might be OK for casual web use, such as social media posts.

Viewed at magnification, the artifacts, loss of detail, and digital 'noise' become apparent.