I usually just lurk, but I felt compelled to offer my opinion here. I'm not a rabbi, but I have studied Jewish law and would like to share my feelings.
The issue is not about animal products; one is allowed to have implants and grafts from any source; leeches, for example, were common in medical use for hundreds of years.
Here, you should take "kosher" to mean whether adjustable gastric band surgery is permissible under Jewish law. While this is a decision to be made between a person and his or her rabbi, I can offer a bit of illumination.
There is one overarching principle in Judaism with regard to medical procedures: life is valued above all else. Elective surgeries are generally frowned upon because of the risk involved. However, one prominent rabbi was known to permit rhinoplasty so that young women could look more attractive and have a better chance of getting married (another important principle in Jewish law). This is certainly not a universal opinion, but there is precedent for it on a purely cosmetic basis for those who wish to have a better chance of finding a mate or enhancing their sex life in a marriage.
The Lap-Band is not inserted for purely cosmetic reasons, and would thus have much more supporting it than a nose job. A procedure that is relatively safe and reduces not just obesity but the complications associated with it, complications that can become life-threatening, should be not just permitted, but encouraged, under Jewish law.
