"… だから" means "because ….". For example, 雨だから遠足は中止になった, which means because of rain, the picnic was canceled. It is often used a lot. …というわけだ means … is the reason. "わけ/訳" represents "reason". We don't use the phrase so much, and it sounds a little literary. For example, 遠足が中止になったのは雨だったからという訳だ, which means "rain is the reason that the picnic was cancelled" . It makes sense, but sounds a little unnatural for me. When we use というわけだ，we use it in novels or TV shows. It is sometimes used to make a sentence or comment more authentic. It's meaning seems to be similar to "I see", "I notice", "I realise", or "I understand "For example. それが犯行の動機だったというわけだ。means "I notice that it is the reason of the crime ".

A=cause, B=effect A だから B=B because (of) A 雨(あめ）だから遠足（えんそく）は中止（ちゅうし）になった。 B というわけだ= That´s why B だから遠足（えんそく）は中止（ちゅうし）になった（というわけだ。）

A=cause, B=effect A だから B=B because (of) A 雨(あめ）だから遠足（えんそく）は中止（ちゅうし）になった。 B というわけだ= That´s why B だから遠足（えんそく）は中止（ちゅうし）になった（というわけだ。）