A discourse connector meaning 'therefore' or 'for that reason,' used to lead to a result or conclusion based on what was just said.
電車が遅れた。そんなわけで、会議に遅刻してしまった。
The train was delayed. For that reason, I was late for the meeting.
彼は病気で来られない。そんなわけで、会は明日に延期になった。
He can't come because he's sick. Therefore the meeting was postponed until tomorrow.
予算が足りない。そんなわけで、計画を縮小することにした。
The budget is insufficient. So we decided to scale back the plan.