The maximum weekly benefit rate for new unemployment claims is rising from $625 to $653. According to the Executive Office of Labor and Workforce Development, the new rate will take effect for claims filed on or after Oct. 2. State law requires the maximum weekly benefit to be revised annually based on the average weekly wage for the 12 months ending March 2011, a period during which the average wage in Massachusetts increased from $1,089 to $1,136. Under state law, the maximum benefit rate equals 57.5 percent of the state’s average weekly wage. Unemployment insurance claimants in Massachusetts receive a weekly benefit of 50 percent of their average weekly wage, up to the maximum amount.