Learn English – What does “slept with a hanger in your mouth” mean

As others have said, it's not a standard phrase. However, it's important to point out how the word heavy can be used to describe things other than weight and mass. Couples can engage in heavy conversations; students can trudge through heavy reading passages. We can be advised not to eat a heavy meal before a long swim.

Your passage doesn't even tell us what is being described – something you should be more careful about in future questions. However, I can venture guess as to what the expression might mean, based on Definition 6 in Macmillan, which says:

heavy (adj.) used about things that look ugly because they are big
heavy features (=large mouth, eyes, and nose) : He was a tall dark man, with heavy features.

As mentioned in the links on that forum thread you found, to channel here means:

4. (transitive) To follow as a model, especially in a performance.
   He was trying to channel President Reagan, but the audience wasn't buying it.
   When it is my turn to sing karaoke, I am going to channel Ray Charles.

The phrase "channel your inner [noun]" is a metaphor, as if there is some "hidden" or "inner" [noun] that you can channel, that is, allow to be expressed more so than it usually would be. For example, if you want to cook a nice meal for your partner, you might "channel your inner chef" and allow that part of you which enjoys cooking good food to be expressed. If you want to pump yourself up before playing in a football game you might "channel your inner warrior."

In this context I would definitely say that the person meant to type "You're just channeling your inner cupcake." A cupcake, literally, is a sweet pastry food; by extension it can be used as an insult:

3. (slang) A weak or effeminate man. [synonyms: cockney, pansy, sissy]

I'm not sure what exactly you said that would cause him to respond like that, but presumably it was not sufficiently "macho."