Blood glucose forecasting models have the potential to improve glycemic control and reduce the burden of diabetes management. However, most prior work has focused on optimizing statistical accuracy, which does not necessarily align with clinical safety and efficacy. This study introduces a clinically weighted root mean squared error (CW-RMSE) loss function that incorporates clinical risk into model optimization by weighting prediction errors according to continuous glucose error grid analysis (CG-EGA) classification and glycemic range to reduce clinically harmful errors. WinFormer, an Informer-based prediction model employing windowed attention, was trained using the REPLACE-BG dataset and either root mean squared error (RMSE) or CW-RMSE loss functions to predict blood glucose values over a 120-min prediction horizon. Compared to RMSE loss, CW-RMSE loss produced significant improvements in CG-EGA classification in hypoglycemia (accurate predictions: 83.2% to 88.0%; erroneous predictions: 13.2% to 8.1%) while maintaining performance for predictions of values in euglycemic (accurate predictions: 92.6% to 92.4%; erroneous predictions: 2.7% to 2.4%) and hyperglycemic ranges (accurate predictions: 91.2% to 90.6%; erroneous predictions: 4.1% to 4.1%). In comparison to RMSE loss, CW-RMSE loss also led to significant improvements in RMSE and mean absolute error (MAE) in hypoglycemia (RMSE: 39.8 mg/dL to 29.8 mg/dL; MAE: 26.6 mg/dL to 16.4 mg/dL), but worse RMSE and MAE in the euglycemia range (RMSE: 31.8 mg/dL to 33.8 mg/dL; MAE: 23.1 mg/dL to 25.1 mg/dL) and the hyperglycemia range (RMSE: 44.9 mg/dL to 52.3 mg/dL; MAE: 30.0 mg/dL to 34.8 mg/dL). These findings demonstrate that cost-sensitive learning can effectively guide blood glucose forecasting models toward more clinically meaningful and risk-aware optimization.