Some computations show that the Weeks manifold and the 5.2 knot complement have the same trace field (which is $\mathbb{Q}[x]/(x^3-x+1)$) and the (hyperbolic) volume of the second is 3 times the volume of the first.

My question is: is there a geometric explanation?

They cannot be commensurable, as one is compact and the other isn't. I also have an algebraic explanation: the Bloch group of the trace field has rank 1, but I would prefer a geometric one, explaining the factor 3.