Please use following results in Billingsley's book: *Convergence of Probability Measures*, 2ed. p.124  Th3.1 p.27. 
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**Theorem** *Suppose that $(X_n,Y_n)$ are random elements of $S\times S$.  If $X_n\Rightarrow X$ and $\rho(X_n,Y_n)\Rightarrow 0$, 
then $Y_n\Rightarrow Y$.* 
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Write 
$$
     W_n(t)=M_n(t)+[W_n(t)-M_n(t)],
$$
Then i) $M_n\stackrel{w}{\to}W$ in Skorokhod topology;  
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ii) $\mathsf{P}(\rho(W_n,M_n)>\varepsilon)\to0$, $\forall \varepsilon>0$, since $\mathsf{E}[\sup_t|W_n(t)-M_n(t)|^2]\to 0$ and
$\mathsf{P}(\sup_t|W_n(t)-M_n(t)|>\varepsilon)\to0$, $\forall \varepsilon>0$. 
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Now by using Th.3.1 and from this two facts it is ready to get $W_n\stackrel{w}{\to}W$ in Skorokhod topology.