In this paper, we introduce a delay-aware largesmall model collaboration scheme for low Earth orbit (LEO) satellite networks, which can balance the computational load among satellites and the communication load across inter-satellite links. Specifically, computational resource constrained remote sensing satellites are responsible for data collection and local processing using small models, while collaborating with computing satellites that provide large model processing. To minimize the service delay, we formulate a joint optimization problem for offloading decision and routing strategy design, which is transformed into a decentralized partially observable Markov decision process. To solve the problem, we develop a multi-agent reinforcement learning (MARL)-based algorithm with offline policy training and online bisection search. The offline trained policy determines routing strategies, while online bisection search iteratively adjusts the offloading decisions. Simulation results demonstrate that the proposed scheme can reduce the service delay by up to 31.85% compared with the benchmarks.