Air Carrier Captain reported a fume event during departure taxi which dissipated. The dirty sock odor resumed more noticeably during climb which prompted in the flight crew to request priority handling for an air return. A safe landing followed.

Narrative

We experienced an odor event with a return to airport. On taxi out there was a slight wet sock odor but it dissipated quickly after second engine start. After takeoff during climb out the flight attendants called us complaining of an odor throughout the cabin. We also noticed the odor and decided to level at 17;000 ft. and take radar vectors to assess the situation. We contacted Dispatch on the local frequency. We originally were planning on returning to ZZZ but at level off the odor started to dissipate. We conferenced with the Flight Attendants and all agreed the odor had dissipated and we agreed to continue on to ZZZ1. Once we started to climb the odor came back. The Flight Attendants reported it smelled like burning crayons. We decided returning to ZZZ quickly was the best course of action. Dispatch was notified. Upon decent we decided to [receive priority] because customers and crew were complaining of headache and dizziness. We reached the gate and did not start the APU considering it may have highly contributed to the odor. I felt the odor was slightly dissipating on arrival into ZZZ. EMS was at the gate to attend to any customers and crew that may have felt symptoms which all of the crew and some customers used.