The Weeksville Heritage Center in Crown Heights in Brooklyn started out operating from a cluster of small wood-frame houses, the remnants of a free black community established in 1838. The organization has preserved those three houses, along with documents and artifacts. Now, a new 23,000-square-foot, $34 million building just yards from the houses presents a chance for Weeksville to create a national showcase for black history and culture.

But at the very moment that Weeksville is poised to elevate its profile, it is struggling. This year, it halved its staff of about 13, trimming their workweek from five days to four and placing some on part-time duty. Its annual budget, once as high as $1.6 million, now hovers around $1 million as funding sources have dwindled. Pamela Green, the executive director since 2001, left this summer to care for her elderly mother in Mississippi. Weeksville tried but failed to get on a list of institutions called the Cultural Institutions Group that the city's Department of Cultural Affairs monitors and supports with financial and technical assistance, although a department spokeswoman said Weeksville receives its support through other channels....