I went on Epinions.com and looked up the specs for the 1986 supra and it shows that the MK3 came in two flavors, the regular Liftback and the Sport Liftback. The sport liftback is shown as ~100lbs lighter then the regular liftback. Were there any differences in the body styles between the regular and sport models?

Targa top, it was also sometimes called a "sport roof", it adds more than 100lbs though.