2 weeks post op, did laser treatment for my spider veins work? (photos)

There are a couple of answers to your question.Firstly, research has shown that leg spider veins (telangiectasia) are different from spider veins above the heart on the face.Because these leg veins are below the heart, they are affected by gravity. 
Published research has shown that 89% of patients with leg spider veins actually have underlying varicose veins. Therefore to make sure you have the best treatment for the spider veins, any vein specialist who is up-to-date with the research would recommend a high resolution venous duplex ultrasound scan first, and fixing any underlying venous reflux (hidden varicose veins) before trying to treat any spider veins on the surface.
The second point is that experience around the world from phlebologist's who deal only with veins shows that the optimal treatment for leg spider veins is Microsclerotherapy rather than laser. Laser on the surface of the leg has a high chance of burning the skin if turned up to the powers required to get rid of the leg spider veins.
There are a few new techniques such as CLACS that suggest a combination of sclerotherapy and laser. However, when you get away from aesthetic practitioners who treat face thread veins similar to leg thread veins and look at the top vein units around the world, the approach is always look for the underlying problem first with venous duplex ultrasound scan, treat that first and then use Microsclerotherapy for thread veins on the surface.

It does take several weeks for the effects of spider vein treatment to be seen.  That said, sclerotherapy (vein injection) is really the best way to treat them.  If they continue to recur or not go away, then you should be evaluated for venous insufficiency or "reflux".  
Good luck