I too have this problem. I set up a scene just like the one in the tutorial. Suzanne knocks over the boxes but changing the mass of either her or the boxes has no effect of the outcome. Suzanne and the boxes are both active not passive objects. Maybe a bug?
Ooops, added a duplicate there. I just made a very similar scene with a ball and 3 boxes. Everything works OK. I can only assume that there is something very subtle about exactly how the scene is built that produces this problem. In the new scene changes in the mass of either the boxes or moving ball have the expected effect. This regardless of whether the values are typed in or applied via 'calculate mass' in the Physics tab. Very odd. If I get to the bottom of it I'll send in another answer.
There's a chance your object collides with boxes while it's in "animated" phase, not dynamic. Just move boxes away (for the main object to be in a "free fall") - that'll do the trick
