Subcritical bubbles can form an appreciable population during weak first-order phase transitions, but are usually treated as isolated fluctuations. This raises the question of whether spatial overlap between neighboring subcritical bubbles can modify their evolution. We address this question by combining analytic free-energy calculations for composite Gaussian profiles with Langevin simulations of overlapping configurations. We find that the overlap lowers the free-energy cost and generally increases the lifetime of subcritical bubbles, with the enhanced persistence potentially feeding back on their abundance. Such overlap can therefore generate collective effects and should be incorporated into kinetic descriptions of subcritical-bubble populations.