Does lifting weights increase the chance that my abdominal aneurysm will rupture?

Maybe: Any activity that increases blood pressure increases the chance that an aneurysm will rupture. Lifting weights that involves straining should therefore be avoided.

Yes: Anything that stresses the arterial wall can predispose to rupture-- typically, high blood pressure, smoking, size of aneurysm are main determinants as well as various collagen disorders. If you cause elevation of your blood pressure by lifting weights, then yes, this could be a risk, depending on other factors.