State of the art controllers for back exoskeletons largely rely on body kinematics. This results in control strategies which cannot provide adaptive support under unknown external loads. We developed a neuromechanical model-based controller (NMBC) for a soft back exosuit, wherein assistive forces were proportional to the active component of lumbosacral joint moments, derived from real-time electromyography-driven models. The exosuit provided adaptive assistance forces with no a priori information on the external loading conditions. Across 10 participants, who stoop-lifted 5 and 15 kg boxes, our NMBC was compared to a non-adaptive virtual spring-based control(VSBC), in which exosuit forces were proportional to trunk inclination. Peak cable assistive forces were modulated across weight conditions for NMBC (5kg: 2.13 N/kg; 15kg: 2.82 N/kg) but not for VSBC (5kg: 1.92 N/kg; 15kg: 2.00 N/kg). The proposed NMBC strategy resulted in larger reduction of cumulative compression forces for 5 kg (NMBC: 18.2%; VSBC: 10.7%) and 15 kg conditions (NMBC: 21.3%; VSBC: 10.2%). Our proposed methodology may facilitate the adoption of non-hindering wearable robotics in real-life scenarios.