Barbara Frietchie's old town hardly ranks as a Big League city - its population is only 40,000 - but it now has its own arts center to serve Frederick county.

If Thursday's official opening of the Weinberg Center for the arts is an indication, Frederick may be joining those modest population clusters across the land presenting professional performers and providing a mart for painters, sculptors and craftsmen from the area.

A sold-out house of 1,180 seats, paying $7.50, $10 and $12, greeted a professional company in "The Robber Bridegroom," a musical new to the Washington area. This is an inventive charmer about Mississippi in the 1790s performed by a bus-and-truck company specializing in one-night stands, but it's worthy of any Washington stage, all of which have seen inferior groups.

The Weinberg Center is in the 53-year-old Tivoli movie house off the main square, outmoded by today's smaller, more economical film theaters. The Weinberg family, which took it over from the Warner chain when film studios were divested of theaters in the late '40s, has given the building.

Mayor Ronald N. Young accepted the gift with the understanding that should it not be used as an art center, it will be returned to the Weinberg family.

"I just don't want it turned into a bowling alley," explains Dan Weinberg, who returned the $19,500 purchase price to the municipality.

Mayor Young placed responsibility for the center on the Arts Council for Frederick City and County, which has delegated management to Kary Walker, co-founder and former spark-plug of Rockville's Harlequin Dinner Theatr.

Opening night found art works throughout the spacious lobbies, including an eye-cathcing "standing painting" by John Wise; oils inspired by the rich farming area that is becoming a bedroom community to Washington; and theatrical memorabilia connected with the Tivoli's early history.

Created three years ago under John Houseman's guidance for The Acting Company of New York, "The Robber Birdegroom" won honors for Alfred Uhry's clever adaption of a novella by Eudora Welty and Barry Bostwick's Tony performance as the Bridegroom. It's a pity Washington hasn't seen it, for lesser works have been booked and Ford's turned Houseman down on its first production.

George DeLoy, of the Broadway production, has risen to Bostwick's showy role and, gifted with a striking presence, does well. If he sticks to his singing lessons, DeLoy has a future.

There was unexpected opening night drama. Rushing from the stage at the end of Act I, leading lady Barbara Marineau broke her ankle, but was effortlessly followed in the second act by Donalyn Petrucci. A measure of the cast's professionalism was Michaelan Sisti's alteration of a line to fit the different hair color of the new heroine. Robert Waldman's music for a stage quartet is country style. Assured performances in the cast of 15 by Laurie Franks, Jared Matesky, Richard Warren Pugh and John Goodman reflected wide experience. Immediately after the performance, the cast set out for its next stop, Scranton, Pa.

Walker has done remarkably well in short order by filling future dates. Coming up: "Grand Ole Opry" this Sunday at 3 and 7 p.m.; Sharon Caplan and "The Washington Ballet," a new company, Feb. 18; Duke Ellington's orchestra, led by the late jazz king's son, Mercer, Feb. 23; and the National Theater of the Deaf, Feb. 25. March 6 will bring a week of free performances by Baltimore's Eastern Opera Theatre in Menotti's "The Medium."