We know it is used in NY, for one weird city, and in many counties for boards of supervisors. Is it used anywhere else? My google searches do not prove fruitful. Jimrtex?
Barnstable County, MA, the Assembly of Delegates is weighted by population. The county government styles itself as the regional government of Cape Cod. There are also 3 county commissioners elected at large, who appear to have executive authority.
Is Barnstable's Weighted Voting System Legal (PDF)It is written by the county counsel, and thus is equivocal.
Bristol, Norfolk, and Plymouth counties in Massachusetts have Advisory Boards whose vote is weighted based on property valuation. Their authority appears to be limited to fiscal matters, though the Norfolk County website suggests that board members be contacted on other matters.
Outside the southeast, county governments in Massachusetts have been abolished. In most cases courts have been continued, but they are legally, district courts with geographical jurisdiction that corresponds to the area of the former county. Some still keep the county as part of the name, but those for Essex, Middlesex, and Worcester are named Eastern, Northern, and Middle.
Corporate governance is usually weighted based on shares owned.
European Council of Ministers is weighted, somewhat on population.