(1) Background: The Strengthening Program for Intensive Developmental Exercises and Activities for Reaching Health Capability (SPIDER) system is dedicated to patients with motor deficits resulting from damage to the peripheral or central nervous system (including post-stroke patients). It enables the conduct of forced-weight-bearing therapy to the lower limb affected by the paresis. In this study, the TYMO® measuring platform was used to quantify the impact of therapy using the SPIDER system and therapy that did not use this system. The TYMO® device is a portable posturography platform that monitors the tilting of the body’s center of mass and reports the results of the rehabilitation process. (2) Objective: To evaluate the effect of therapy based on neurophysiological methods (proprioceptive neuromuscular facilitation (PNF), neurodevelopmental treatment according to the Bobath concept (NDT-Bobath)) and the SPIDER system on body weight transfer shifting, in post-stroke patients in the chronic phase, compared to therapy based on neurophysiological methods (PNF, NDT-Bobath), without the use of the SPIDER system. (3) Methods: This is a randomized controlled trial in which patients (n = 120; adults, post-ischemic stroke—first stroke episode, in chronic phase—up to 5 years after the stroke incident) were assigned to one of two groups: study, n = 60 (with therapy using PNF, NDT-Bobath methods and the SPIDER system); and control, n = 60 (with therapy using PNF and NDT-Bobath methods, without the SPIDER system). In patients in both groups, before and after the training (2 weeks of therapy), body weight distribution was measured on the TYMO® platform. (4) Results and Conclusions: The results of the statistical analysis demonstrated a greater reduction in the tilt of the body’s center of mass in therapy using the SPIDER system, compared to therapy in which the system was not used.