I think it is the actual file size not the pixel size that matters as the screenshot shows.
I guess when you reduced the pixel size of your image that reduced the file size. If you want to keep the pixel size you can always save the jpeg to a greater compression. You will loose a little quality but so long as you don't go too far that probebly wont notice on anything but the very highest grade monitor. i don't know what Photo editor you use but when you hit thesave button you should get the choice of saving the image to a certain compression either from 1 to 10 or sometimes 1 to 12. If you save at about half way say 5 or 6 then that will give a reasonable quality with a small file size. This is the way to keep the file sizes down but keep the picture size high when you want to send an image by email!