The scope of this work is to show the applicability of the Twisted String Actuators (TSAs) for lightweight, wearable and assistive robotic applications. To this aim, we have developed a novel surface electromyography (sEMG)-driven soft ExoSuit using the TSAs to perform both single and dual-arm elbow assistive applications. The proposed ExoSuit, with an overall weight of 1650 g, uses a pair of TSAs mounted in the back of the user, connected via tendons to the user's forearms to actuate each arm independently for supporting external loads. We confirm this new light-weight and customizable wearable solution via multiple user studies based on the biceps and tricep' sEMG measurements. We demonstrate that user's muscles can automatically activate and regulate the TSAs and compensate for the user's effort: by using our controller based on a Double Threshold Strategy (DTS) with a standard PID regulator, we report that the system was able to limit the biceps' sEMG activity under an arbitrary target threshold, compensating a muscular activity equal to 220% (related to a single arm 3 kg load) and 110% (related to a dual arm 4 kg load) of the threshold value itself. Moreover, the triceps' sEMG signal detects the external load and, depending on the threshold, returns the system to the initial state where it requires no assistance from the ExoSuit. The experimental results show the proposed ExoSuit's capabilities in both single and dualarm load compensation tasks. Therefore, the applicability of the TSAs is experimentally demonstrated for a real-case assistive device, fostering future studies and developments of this kind of actuation strategy for wearable robotic systems.