Patronage on the Metro subway since it opened for nighttime service this week is exceeding expectations, with as many as 12,000 additional riders using the late trains, the transit authority reported yesterday.

Before the subway operating hours were extended from 8 p.m. to midnight on Monday, Metro planners had estimated that 9,000 more people would ride the trains - but only after several weeks of patronage build-up.

On Monday, the first night, an estimated 5,000 additional passengers rode the trains, Nicholas J. Roll, acting general manager, told the Metro board yesterday. On both Tuesday and Wednesday nights, Metro figures showed, 12,000 more passenger rode.

Both Tuesday and Wednesday, total all-day ridership - from 6 a.m. to midnight - on the two subway routes exceeded 197,000, close to the record 204,000 recorded at the peak of the spring tourist season.

Beginning tomorrow, Metro will begin operating subway trains on Saturdays, from 8 a.m. to midnight, with the flat 50-cent offpeak fare to be charged for all rides. There will be no train service on Sundays for now.

Next Monday, Metro will provide its first train service to a football game at the Robert F. Kennedy Stadium, where the Washington Redskins will play the Dallas Cowboys.

If the game goes into overtime or is delayed beyond midnight for any reason, Roll said, the hours of train service will be extended so that no football fan will be stranded.

Metro will park six eight-car trains on the tracks north of Stadium-Armory station and will dispatch as many as are needed to handle the crowd. The trains have a capacity of 9,000 passengers.

Also at yesterday's meeting, the Metro board was told by Donald R. O'Hearn, director of program control, that the delay in subway construction caused by the restudy of the rail system's future route layout added $222.8 million to the cost of the 101-mile system.

The restudy was required by the U.S. Department of Transportation and resulted in a decision to push for completion of the entire 10-mile system rather than a truncated version. The cost of the full system is now estimated at $6.7 billion.