Above-barrier cross sections of α-active heavy reaction products, as well as fission, were measured for the reactions of 10,11 B with 209 Bi. Detailed analysis showed that the heavy products include components from incomplete fusion as well as complete fusion (CF), but fission originates almost exclusively from CF. Compared with fusion calculations without breakup, the CF cross sections are suppressed by 15% for 10 B and 7% for 11 B. A consistent and systematic variation of the suppression of CF for reactions of the weakly bound nuclei 6,7 Li, 9 Be, 10,11 B on targets of 208 Pb and 209 Bi is found as a function of the breakup threshold energy.