The internet ate my post.
The manual refers you to the sticker on the doorjamb. So my BRZ Limited with a Manual has a GVWR of 3682.
If you're looking for an actual weight, I believe a similarly equipped BRZ was weighed at 2715 with 1/4 tank and no driver. Premium BRZs and the FR-S should come in lighter. Automatic transmissions will increase the weight.