All current plans for deep space missions use water (and human waste) as radiation shielding. The heaviness isn't an issue because we tend to need water when we go on long isolated trips. So you have to bring it with you and it is exceptional at blocking radiation and far, far superior to concrete. Concrete is only good because it has high water content and density.

"Concrete is a relatively cheap material and easy to be cast into variously shaped structures. Its good shielding properties against neutrons and gamma-rays, due to its intrinsic water content and relatively high-density, respectively, make it the most widely used material for radiation shielding also."