We study the spreading of a droplet of surfactant solution on a thin suspended soap film as a function of dynamic surface tension and volume of the droplet. Radial growth of the leading edge (R) shows power-law dependence on time with exponents ranging roughly from 0.1 to 1 for different surface tension differences (Delta sigma) between the film and the droplet. 'When the surface tension of the droplet is lower than the surface tension of the film (Delta sigma > 0), we observe rapid spreading of the droplet with R approximate to t(alpha), where alpha (0.4 < alpha < 1) is highly dependent on Delta sigma. Balance arguments assuming the spreading process is driven by Marangoni stresses versus inertial stresses yield alpha = 2/3. When the surface tension difference does not favor spreading (Delta sigma < 0), spreading still occurs but is slow with 0.1 < alpha < 0.2. This phenomenon could be used for stretching droplets in 2D and modifying thin suspended films.