Are any veins too big to be treated non-surgically?

The short answer is no. In the past (and sadly still now) some surgeons claimed that if the veins were very big then surgery was the only treatment that worked. This is not true. When Ultrasound Guided Sclerotherapy was the only non-surgical treatment available, it could be said that it was an inefficient was of treating very large veins because multiple treatments would often be required to get the desired result. This has all changed with the advent of Endovenous Laser Ablation where the size of the vein is not a limiting factor because of the way the vein is treated.