What can I do to increase the size of my masseter muscles?

You are not going to increase the size of your masseter muscles by any form of non-surgical therapy. Since you are opposed to implants, the other option to consider is fat injections placed directly into the muscle. While this is a minor surgery, it is a natural non-implant approach.

If you are having TMJ issues or trouble chewing your food a TMJ specialist prior to your starting on an exercise program should evaluate this. If your issue is aesthetic there are different options. Like any muscle you can exercise it to increase its strength and tone. I doubt that you could enlarge it significantly to change your aesthetic contour; and if you did it might not be the aesthetic result your are desiring. I do not have any experience in exercising masseter muscles.Fillers can change soft tissue contour are very popular and help to balance and aesthetically improve the shape or your face. Performed correctly they can restore the changes for aging and refine the qualities you want.