I just realised that the collective weight of all the missiles would weigh 6000 tons. Which is more than my mech as a whole. 

You are hereby safe to assume that some kind of super science mumbo jumbo is in play to lighten that load. Dimensional subspace tubes or whatever.

Edit: Also, posted. Super tired, so let me know if I missed something, or if sense was not made. You know, besides the weight paradox.