This study investigated the size effect of steel tube and sandwiched concrete jacketed CFST columns under eccentric compression. A series of eccentric compression tests were conducted on 3 geometrically similar un-strengthened CFST columns and 13 strengthened CFST columns with varying structural sizes (with a ratio of 1:1.5:2), different eccentricities, and different outer steel ratios. The eccentric performance of the specimens, including their failure behaviours, load-axial displacement curves, and longitudinal and circumferential strain distribution were explored. Additionally, the size effect on nominal stress-longitudinal displacement relationships, nominal axial strength, nominal ultimate deflection and ductility index were investigated. The test results confirmed the presence of a size effect in both un-strengthened and strengthened CFST columns, with nominal strengths closely following Bažant's proposed "size effect law (SEL)". Finally, considering the influence of size effect, this study proposed axial force-bending moment (N-M) correlation curves for predicting the bearing capacity of strengthened CFST stub columns based on EC4, AISC-360, AIJ and GB 50936. Among these codes, AIJ provided the most accurate predictions when compared to the test results. Introducing the size effect coefficients mitigated the tendency to overestimate the load-bearing capacity of large-size retrofitted columns.