Why do nonmetal oxides react with water to form acidic compounds?
Well, in terms of this reaction, sulfur in $\ce{SO3}$ acts as a Lewis acid for an incoming $\ce{OH-}$ nucleophile. The reaction mechanism seems to be any old nucleophilic addition reaction:


$\ce{H2O &lt;=&gt; H+ + OH-}$ : (Water can disassociate into its ions)
$\ce{SO3 + OH- -&gt; SO2(OH)O-}$ : (I couldn't decide on whether this is the right 
way to write this intermediate, but I'll be happy to add a diagram for clarity)
$\ce{SO2(OH)O- + H+ -&gt; SO2(OH)2}$ : (This is the final step of the mechanism to yield $\ce{H2SO4}$)