If an airplane has a 2.5G load limit (ignoring for now any safety factors), the WING will not likely failwith any load up to 2.5 x max gross takeoff weight. HOWEVER, individual components may only be stressed to 2.5G, so a 3G stress will break them.
An example I read in a magazine many years ago was the battery shelf on a light SE airplane. If the airplane was limited to 4G, then the battery shelf was likely designed to a 4G limit. Even if the wings could withstand 5G at light gross weights, that battery shelf would break, and may cause catastrophic consequential damage.