Embodied robotic systems increasingly rely on large language model (LLM)-based agents to support high-level reasoning, planning, and decision-making during interactions with the environment. However, invoking LLM reasoning introduces substantial computational latency and resource overhead, which can interrupt action execution and reduce system reliability. Excessive reasoning may delay actions, while insufficient reasoning often leads to incorrect decisions and task failures. This raises a fundamental question for embodied agents: when should the agent reason, and when should it act? In this work, we propose RARRL (Resource-Aware Reasoning via Reinforcement Learning), a hierarchical framework for resource-aware orchestration of embodied agents. Rather than learning low-level control policies, RARRL learns a high-level orchestration policy that operates at the agent's decision-making layer. This policy enables the agent to adaptively determine whether to invoke reasoning, which reasoning role to employ, and how much computational budget to allocate based on current observations, execution history, and remaining resources. Extensive experiments, including evaluations with empirical latency profiles derived from the ALFRED benchmark, show that RARRL consistently improves task success rates while reducing execution latency and enhancing robustness compared with fixed or heuristic reasoning strategies. These results demonstrate that adaptive reasoning control is essential for building reliable and efficient embodied robotic agents.