Because JPEGs are compressed, the file size depends on both the dimensions (in pixels) and the amount of detail in the photo - the more detail, the less it can be compressed.
In PSP, if you Save As and choose JPEG, there is an Options button which lets you set the JPEG quality - i.e. the amount of compression - on a scale from 1 to 100 where 1 is theoretically lossless.
For high quality I suggest setting this to 5. For the web, if you need to reduce file size, you can go down to 15 or even 20 without any noticeable deterioration.
Once you have set this parameter, it is remembered for all future JPEG saves until you change it again, so remember to revert to 5 next time you want high quality.
EDIT/ Oops - I got the figures the wrong way round - low is best - now corrected.