According to Advisory Circular AC68-1A:
5.1.2 Type Certificated Aircraft. For type certificated aircraft, the aircraft’s design approval would authorize the number of occupants the aircraft may carry and would contain the maximum certificated takeoff weight. The aircraft’s design approval may be a type certificate (TC), a supplemental type certificate (STC), or an amended TC (ATC). The FAA recognizes that changes could be made to an aircraft’s type design. For example, an aircraft type certificated to carry more than six occupants may be altered to carry six or fewer occupants. In order to make such a change, that aircraft would have to obtain a new design approval, such as an STC or an ATC. So long as an aircraft’s design approval (i.e., TC, STC, or ATC) authorizes the aircraft to carry no more than six occupants, that aircraft would meet the requirements of § 61.113(i)(1). Additionally, if an aircraft with a maximum certificated takeoff weight of more than 6,000 pounds is altered to have a maximum certificated takeoff weight of less than 6,000 pounds, then that aircraft would likewise meet the requirements of § 61.113(i)(1).
(italics mine) So yes, you can fly under basicmed with an aircraft that has had the weight reduced by STC, or removal of an STC. It doesn't have the stupid "continuously met the requirements" of Sport Pilot/LSA.