Backscatter communication (BSC) is emerging as the core technology for pervasive sustainable internet-of-things applications. However, owing to the resource-limitations of passive tags, this work targets at maximizing the achievable sum-backscattered-throughput by jointly optimizing the transceiver (TRX) design at the full-duplex multiantenna reader and backscattering coefficients (BC) at the single antenna tags. Despite this joint optimization problem being non-convex, we present low-complexity joint TRX-BC designs by exploring the asymptotically-optimal solutions in low and high signal-to-noise-ratio regimes. We discourse that with precoder and detector designs at the reader respectively targeting downlink energy beamforming and uplinkWiener filtering operations, the BC optimization at tags can be reduced to a binary power control problem. Selected computer simulations are presented to validate the analytical claims, shed optimal-design insights, and demonstrate the throughput enhancement of around 20% over the relevant benchmark schemes.