You must be looking at something other than I see.  I open a 1.6 meg jpeg file (bridge metadata) into PS.  I then click Save As and click save when the window comes up.  It then asks for the quality.  At a setting of 10 the file size would be 1 meg,  and even if I ramp it up to 12 the file size is 2.2 meg.  (file size adjusts to the new quality setting but may take a second or two to compute)

When you say the size almost doubles where are you seeing these numbers?

Property tab of what? 

Resoluton in ppi has nothing to do with save quality in jpeg.  The quality changes depending on how many pixels you want to throw away to get a smaller file size.

Every time you save a jpeg it looses quality as it is being recompressed.  You can not gain quality so just because the size is larger than the original does not mean it is a higher quality. 

If you want to save with highest quality use TIFF or PSD, but the file sizes will be considerably larger.

Since I can not see what you see perhaps a screen shot of the 4.8 meg file opening as a 8 meg file would help.  As it only makes sense that it will open as a 4.8 meg file.

If you are not getting what I am writing you need to do a web search for "saving a jpeg".  Here is an excerpt from one.

But don't get too hung up on loss of quality, as if you save at quality 8 or above you will never see it unless your edit and resave may times.  I save at quality 9.

JPEGs lose quality every time they are opened, edited and saved.

If a JPEG image is opened, edited, and saved again it results in additional image degradation. It is very important to minimize the number of editing sessions between the initial and final version of a JPEG image. If you must perform editing functions in several sessions or in several different programs, you should use an image format that is not lossy (TIFF, BMP, PNG) for the intermediate editing sessions before saving the final version. Repeated saving within the same editing session won't introduce additional damage. It is only when the image is closed, re-opened, edited and saved again.