The All England Lawn Tennis and Croquet Club wants to treble the size of its main site, which has been home to the Championships since 1877, in a £200 million project which would feature 39 new courts.
The AELTC's plans to redevelop a former golf course which it owns are supported by several leading players and some local residents.
But campaign group Save Wimbledon Park, which took legal action to challenge planning permission, argues the land is subject to a statutory trust meaning it must be kept for public recreation.
The AELTC is seeking a ruling from London's High Court that the land is not subject to such a trust, with its lawyers saying it has never been used for public recreation.
Dozens of Save Wimbledon Park's supporters gathered outside court before Friday's hearing, including two women dressed as tennis balls holding a sign which said: "Balls to AELTC."
The expansion plans were at the centre of a separate case last summer, when Save Wimbledon Park challenged planning permission approved by the Greater London Authority in 2024.
Save Wimbledon Park argued in that case that the GLA failed to properly take account of restrictions on redeveloping the land. Their challenge was rejected, but the group has since been granted permission to appeal against that ruling.