Accurate and cost-effective quantification of the agroecosystem carbon cycle at decision-relevant scales is essential for climate mitigation and sustainable agriculture. However, both transfer learning and the exploitation of spatial variability in this field are challenging, as they involve heterogeneous data and complex cross-scale dependencies. Conventional approaches often rely on location-independent parameterizations and independent training, underutilizing transfer learning and spatial heterogeneity in the inputs, and limiting their applicability in regions with substantial variability. We propose FTBSC-KGML (Fine-Tuning-Based Site Calibration-Knowledge-Guided Machine Learning), a pretraining- and fine-tuning-based, spatial-variability-aware, and knowledge-guided machine learning framework that augments KGML-ag with a pretraining-fine-tuning process and site-specific parameters. Using a pretraining-fine-tuning process with remote-sensing GPP, climate, and soil covariates collected across multiple midwestern sites, FTBSC-KGML estimates land emissions while leveraging transfer learning and spatial heterogeneity. A key component is a spatial-heterogeneity-aware transfer-learning scheme, which is a globally pretrained model that is fine-tuned at each state or site to learn place-aware representations, thereby improving local accuracy under limited data without sacrificing interpretability. Empirically, FTBSC-KGML achieves lower validation error and greater consistency in explanatory power than a purely global model, thereby better capturing spatial variability across states. This work extends the prior SDSA-KGML framework.