The best thing to do is to get a diagnostic venous duplex scan (doppler and ultrasound) where the veins can be mapped and a determination is made as to whether you have uperficial venous insufficiency which can be fixed either with foam clerotherapy, VNUS CLosure, endovenous laser therapy (EVLT) or ClariVein. Find a physician group like mine which provides ALL of these treatments so that you have options. Good luck. You can read my ebbok for free on the link below.
Varicose veins are due to malfunctioning (leaking) valves of the saphenous system. If you have varicose veins they can enlarge with exercise as more blood flows through them. You should see a vein specialist for a full venous evaluation to determine the status of your venous valves. This is done with a venous reflux exam. If your veins are not treated, then they will worsen with time. You do not need to stop exercising.
Physical exertion does make them looking bigger, but does not cause or contribute to their development. So, don't stop working out, but have them professionally evaluated by a specialist.