Why is sodium sulfate a neutral salt
For a solution of $\ce{Na2SO4}$, the sodium sulfate will ionize as you indicated:


  
    $\ce{Na2SO4(s) -&gt;[aq] 2Na+(aq) + SO4^{2-}(aq)}$
  


This reaction is essentially irreversible in that the ions in an unsaturated solution won't suddenly form solid $\ce{Na2SO4}$ again. 

$\ce{HSO4-}$ is a not a weak acid, but has a $\text{pK}_\text{a2} = 1.99$ which makes a moderately strong acid. So for  pH > 3 essentially all the $\ce{HSO4-}$ will ionize:


  
    $\ce{HSO4-(aq) + H2O -&gt;[pH &gt; 3] H3O+ (aq) + SO4^2- (aq)}$
  


Thus $\ce{SO4^{2-}}$ is such a weak base that reverse reaction doesn't happen when you dissolve $\ce{Na2SO4}$, and a solution of $\ce{Na2SO4}$ in distilled water stays neutral rather than becoming basic. 


  
    $\ce{\require{cancel}H2O + SO4^2- \cancel{-&gt;} HSO4- + OH-}$
  


To think about a different example acetic acid is a weaker acid, $\text{pK}_\text{a} = 4.76$, so the acetate anion is a stronger base than the sulfate anion. A solution of sodium acetate would become weakly basic. 

One last point - the statement should be "sodium sulfate a neutral salt in aqueous solution." In other solvents sodium sulfate could act as a base.