Board Thread:Misc./@comment-27255656-20170508190720/@comment-14745711-20170517034006

Presumably not very much, as we know Titans are supposed to be bizarly light for their immense size and strength. Assuming the hardened parts of a Titan are heavy, the Armoured Titan might weigh a fair bit. It's clear the Colossal is also heavy since he leaves large footprints on both occasions where he destroys a gate, though this could just be due to him being so massive. Perhaps Titan shifters are an exception and are actually heavy? But there's besides said footprints for the Colossal Titan there's no reason to think that.

So I guess the best answer to your question that can be given is, not much?