How does gross weight affect the Minimum Controllable Airspeed (Vmc)?
I think your objection to #2 is exactly correct, and your #1 is where the misunderstanding may lie.

The point of VMCA is essentially to maintain a constant heading, and when you have no more rudder authority to make that happen, you're there -- and any slower, with slightly less rudder authority, your heading starts to change in the direction of the dead engine.  With no bank, it's all rudder; the lift from the wings doesn't tend to move the nose in any direction.  With bank, there is now a component of the lift from the wings that does tend to affect heading (which is the dynamic of banking when you turn -- the heading change comes from the lift created by the wings, not from the lift generated by the rudder).  

If you are banking into the good engine, that component of lift tends to change your heading toward the good engine and away from the failed engine.  Since the asymmetric thrust is working to change your heading toward the failed engine while you hold rudder to oppose that change, you now have the component of lift from the wings that is assisting your rudder.

If you consider a case of symmetric thrust, you can hold a heading with right wing down and left rudder or vice versa; the lift from the wings is working to change your heading to the right, and your rudder is counteracting that drift. At some point, with enough bank, you run out of rudder authority &amp; the airplane will turn, although pretty badly uncoordinated.  With an engine out, you CAN fly straight ahead holding bank into the dead engine, you just need a lot of rudder authority (i.e. lots of speed above VMCA) to hold your heading -- the rudder is fighting both the asymmetric thrust and the component of the wings' lift. And doing that, you'll run out of rudder authority a lot sooner (i.e. at a higher airspeed).  If you switch to bank into the good engine, the component of lift from the wings is now working with you, and that's the usual case for computing and demonstrating VMCA.

I suspect that the confusion on your point #1 comes by conflating horizontal (earth reference) with horizontal (aircraft reference). Hopefully the explanation above separates things out?

And, to bring things back to gross weight, the higher the weight, the greater the lift from the wings, so a Sin(5 degrees) (I think that's right -- LONG time since I took Trig!) component of "more lift" is a greater force to resist heading change than that same component of "less lift" with a lighter aircraft.  The other forces involved in the balance, the asymmetric thrust and the rudder force, are independent of aircraft weight.

Best wishes for your MEL checkride!