A tendon is provided for supporting a balloon having a balloon envelope. The tendon has first and second end portions that are configured to be secured to sections of the balloon envelope and a main body portion disposed between the ends. The main body portion is configured to support a load caused by inflating the balloon envelope. The first end, second end and main body portions are formed from a plurality of weft and warp fibers disposed as webbing. The warp fibers extend longitudinally through the webbing and the weft fibers extend threadedly from side to side through the warp fibers. An elasticity of the tendon is adjusted by configuring the weft fibers along a particular weft path so as to be spaced apart in the main body portion at a certain distance from each other that is different than a spacing of the weft fibers in the ends.