Machine Learning (ML)-based optimization approaches emerge as a promising technique for solving large-scale Mixed Integer Linear Programs (MILPs). However, existing ML-based frameworks suffer from high model computation complexity, weak problem reduction, and reliance on large-scale optimizers and large training datasets, resulting in performance bottlenecks for large-scale MILPs. This paper proposes Light-MILPopt, a lightweight large-scale optimization framework that only uses a small-scale optimizer and small training dataset to solve large-scale MILPs. Specifically, Light-MILPopt can be divided into four stages: Problem Formulation for problem division to reduce model computational costs, Model-based Initial Solution Prediction for predicting and constructing the initial solution using a small-scale training dataset, Problem Reduction for both variable and constraint reduction, and Data-driven Optimization for current solution improvement employing a small-scale optimizer. Experimental evaluations on four large-scale benchmark MILPs and a real-world case study demonstrate that Light-MILPopt, leveraging a small-scale optimizer and small training dataset, outperforms the state-of-the-art ML-based optimization framework and advanced large-scale solvers (e.g. Gurobi, SCIP). The results and further analyses substantiate the ML-based framework's feasibility and effectiveness in solving large-scale MILPs.