B767 Captain reported Flight Attendant and passenger illnesses resulting from cabin fumes during cruise. The flight diverted and performed an overweight landing.

Narrative

Flight ZZZZ1-ZZZ. Aircraft X. Approximately 10 minutes after takeoff the purser advised me that one of the flight attendants was feeling dizzy and nauseated. They identified two medical volunteers who were assisting the flight attendant with therapeutic oxygen and he was sitting in his jumpseat. She also mentioned as we took off the aft galley noticed an odor of fumes but that they dissipated after we were in the air. Approximately 10-15 minutes later she called back to say the two assisting passengers were beginning to feel similar symptoms. We called Medlink via SATCOM to consult with the physician. F/A Person A; and passengers in 22K and 22L. Medlink advised to provide therapeutic oxygen for 30 minutes and to offer anti nausea medication. Over the next thirty minutes three more flight attendants began to experience like symptoms. Person B; Percon C; and Person D began administering themselves oxygen. Conferred again with Medlink and Dispatch and updated them on the developments with the F/As and oxygen. Person A who had been on oxygen for 35 mins wasn't improving. With this info it was decided to divert to ZZZZ. Priority handling was requested and we proceeded to ZZZZ. We landed approximately 15 minutes later at approximately 40K lbs over max landing weight. Exiting the runway the flight attendants reported the odor of fumes again. We filed an ELB (Electronic Log Book) consisting of overweight landing; odor of fumes aft galley; FRK (First Response Kit) used; 6 bottles of oxygen used; and F/A interphone to cockpit notifications inop. After a layover in ZZZZ; we ferried Aircraft X to ZZZ.