Weber focuses on three dimensions of power that are class, status and party.
So the idea of race would most probably fall into the category of status. Status refers to an effective claim to positive social esteem. Powerful groups claim positive social honor and privileges for themselves and at the same time impose negative social honor and privileges on less powerful groups. Almost allstatus honors of groups rely on the idea of usurpation. Usurpation is the claiming of social honor through the illegal use of force. The primary motivation a group has for claiming social honor is usually to monopolize economic and political opportunities for members of the status group. After positive status honor is gained, it is much easier to set laws that assure positive privilege for positive status groups and impose negative privilege for negative status groups.
So, if we were to talk about a capitalist economy, Weber would state that chances determine ones class nothing having to deal with race, gender, ect … but sadly even after the civil rights movement, the U.S still has unspoken institutionalized racism were being in a high class wont necessarily mean one is getting the honor and privileges that usually go along with it.