Some of the software applications you can use to convert jpg files are:
If you are going to be working with images, you should have a good image program installed in your computer so that you can handle the task properly. Relying upon online or barebones services will give you low quality images.
The whole purpose of using jpg compression is so that your images are not overly large for their purpose.
If you are a professional photographer and are showing off your work, you might want high quality / high bandwidth images so that your readers can see the quality of your work.
For most others, compression is far more important so that the images will load quickly and not hog bandwidth.
An application like "The Gimp" gives you the flexibility to decide upon the level of compression (85% is usually great for most uses) and this will have a huge impact on your file size. Read more about "The Gimp".
Do you know when to save an image as a .jpg and when to save it as a .gif or .png?