Weak-grid rural settlements in remote areas often face fragile grid infrastructure and high fuel transportation costs, which severely limit both the economic performance and operational reliability of local energy systems. While the rapid growth of renewables helps reduce reliance on fossil fuels and strengthens resilience through multi-energy complementarity, the natural variability of wind and solar power becomes much more problematic in weak-grid settings, driving up energy supply risk costs. To tackle these issues, this paper presents a two-stage scheduling framework for weak-grid integrated energy systems (IES). The framework brings demand-side airborne wind energy (AWE) into the system to capture more stable high-altitude wind resources, with power output regulated by adjusting altitude. A double-loop modeling approach allows both the AWE operating height and its power output to take part directly in optimal scheduling. At the same time, a virtual-battery-based demand response mechanism is used to represent load flexibility. Uncertainties are addressed with a Wasserstein distance-driven distributionally robust optimization (DRO) model that includes Conditional Value-at-Risk (CVaR) to quantify tail risks and balance costs against extreme scenarios. Validation on a township-level energy system in Hami, Xinjiang, China, based on five comparative experiments and sensitivity analysis, shows that the proposed framework cuts total operating cost by 3.67% and reduces tail risk loss (CVaR, α = 0.90) by 7.52% compared with the baseline, with the virtual battery-based demand response contributing an extra 10.3% cost saving. Overall, the framework offers a practical and scalable approach for integrating high shares of renewables in weak-grid regions, markedly improving renewable accommodation and the system’s ability to withstand disturbances.