Pinching antenna systems (PASS) enable reconfigurable radiating elements and extended line-of-sight communication, mitigating path loss effects. However, existing designs lack fully controllable radiation weights, as they are governed by structural parameters rather than explicitly assigned variables. In this paper, we introduce a new degree of freedom (DoF) for PASS by enabling radiation weight control through phase-mismatch manipulation of guided waves under single-mode excitation within a coupled-mode framework. By tuning the propagation constants of pinching antennas, independent complex-weight control of individual elements is achieved, transforming PASS into a weight-adaptive analog beamforming architecture. Based on this principle, we present a physics-based hardware model that provides a unified framework for both amplitude-tunable pinching beamforming and conventional equal-power radiation models, ensuring compatibility with existing PASS implementations, such as movable setups. To evaluate the proposed model, we formulate a sum-rate maximization problem for hybrid precoding in multiuser downlink systems and solve it using an alternating optimization framework that combines weighted minimum mean square error-based digital precoding with genetic algorithm-based optimization of PASS configurations, including various scenarios such as weight tuning, antenna movability, and discrete activation. Numerical results demonstrate that the amplitude-tunable PASS architecture achieves consistent performance gains over conventional arrays and existing PASS schemes, with pronounced improvements in interference-limited regimes under practical constraints.

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