Will the veins come back if I lift weights at the gym?

venous insufficiency at the saphenofemoral junction can worsen with weight lifting - as bearing down to lift or doing  Valsalva maneuver, will increase intraabdominal pressure and force blood to leak from deep veins into superficial veins - hence, venous insufficiency. Topical products containing horse chestnut extract will promote vein health (see link below). 

This will largely depend upon how they were treated, not what you do. Compression for 2-3 weeks immediately following treatment offers the best chance of cure. At that point, it all depends upon the veins.If small spider veins were treated with sclerotherapy there is a chance they will come back over the years. In addition, new veins can appear for the same reason the original veins appeared. Surgical removal of large veins is one of the few absolutely permanent solutions. However, small veins may still appear in the treated area.

It depends on, first, what kind of veins you had and, second, what type of treatment you underwent. In general, if the condition responsible for formation of your veins was not cured, they do come back regardless of weight lifting.

Spider veins tend to recur over time and the treatment of these spider veins should be considered as a maintenance issue. They can be affected by many things including genetics, aging and sun exposure. Varicose veins are the result of malfunctioning (refluxing) valves usually of the saphenous system. If the valves have been treated then the varicose veins should not return. There is controversy with regard to exercise as to what exercise can increase veins. In general, exercise is good for veins but pounding such as running or weight lifting which increases the intraabdominal and intrathoracic pressure is not.