Do I have a weak jawline and should I get jaw surgery to fix my under bite? (Photo)

The important question is how signifcant your underbite and of you are going to do anything with it. Since you have had orthodontcis twice my assumption is that your bite relationship is set and jaw advancement surgery is not on the table. Thus you can just focus on your chin. Your chin is horizontally short but somewhat vertically long. This rules out an implant since that will keep your chin vertically long and may even appear longer than it is now. You will need to consider a sliding genioplasty which will bring your chin but can shorten it as well.The potential benefits can be seen by having some computer imaging done of this type of facial profile change.

I actually see a slight deficiency in the upper jaw.  If you notice, there is a flatness of skin around the base of your nose.  By bringing the upper jaw forward, you will get a better support in that region, look younger,  your nose will not look as big as you think, and you under-bite would be corrected.