I found your theory on the moon, and its symbology in the RWBY trailers, and I was really intrigued by the ideas you brought up! But the more I thought about it, the less convinced I was about it. The reasons for this are twofold; first that I doubt the intent was to tie Weiss symbolically to the moon, and secondly that its symbolic weight is more metaphorical in nature. The key thing that leads me to both conclusions, is the songs of RWBY.
See, Weiss has roughly half a dozen character songs scattered through the first five volumes (though oddly, I can't think of any after volume five) and there's a lot of common themes running through them; namely, Weiss' struggle with identity and being denied agency or dreams. In most of them, the mirror exists as a rhetorical device for her to voice her thoughts to- and the way she speaks to it makes it pretty clear it's actually analogous to Jacques in the later songs. The moon doesn't feature at all, which is something I'd expect from character songs tied to someone who is symbolically linked to the moon.
There is one line in Path to Isolation that could be referencing the moon, but in context it's pretty clearly not about Weiss herself, but rather the sudden sundering of her family when she was ten. (The line in question being "The light that showed the way is gone", which I'm noting now because it's important to the other half of my thoughts.)
Now, the moon is directly referenced in a bunch of songs in the first three volumes, namely: I May Fall, Die, Sacrifice, and When It Falls. In most songs, the moon either crumbles, shatters, or disappears in some way. There are two exceptions to this, both featured among the songs I selected, but I want to cover the main way the moon is referenced first.
Here is how it appears in I May Fall:
"When we lose our faith
And forsake our friends
When the moon is gone
And we reach our end"
And here is its appearance in When It Falls:
"Swallowed by the darkness
Soon the moon is bathed in black
The light of hope is taken
And discontent is the contagion"
And for good measure, here's how it appears in the chorus of Die:
"Feel it everywhere and you see it growing,
Enemies arise and the hate is flowing,
Shattering the moon and bloodying the sky."
All taken together, the common theme shows the moon being destroyed or obscured as a symbol of division, of hatred, despair creeping in to replace the light. Considering the original shattering of the moon happened right after the Brother of Darkness destroyed humanity, it feels like a likely idea to land on, right?
When I have more time, I'd like to investigate whether I can find a link between growing distrust/despair to views of the shattered moon, and views of its whole side alongside hope and unity, in the show proper. That would be a massive undertaking though, probably best saved for when I finally get around to a rewatch.
Now, for the exceptions I noted within the songs. Here's the moon at the beginning of Die:
"Our dreams came true,
Our path was clear,
The moon watched safely from above."
"Born an angel, heaven sent,
Falls from grace are never elegant.
Stars will drop out of the sky,
The moon will sadly watch the roses die."
The exact meaning of these lyrics isn't exceedingly important (though Sacrifice represents another hit against Weiss being the moon; she only knows of Summer from what Ruby has said, and to my knowledge wasn't privy to any of Ruby's visions regarding her mother) but what is important here is that the moon has been established as something that watches over people. This ties into something I've concluded from looking at all the songs that reference the moon in volumes 1-3, because while I think the moon itself is a symbol of unity, friendship, and hope, I believe the songs have the moon standing in for something more specific.
Namely, Beacon Academy. It has one of the CCT towers, one of the biggest symbols of unity the people of Remnant have ever constructed, and as the premier Hunter Academy, it is a bountiful symbol of hope. Its destruction sends the whole of Remnant into a spiral of distrust, hatred, despair, and division. The songs abruptly stop referencing the moon at all volume four onward, with only one direct mention in Rising, where the reference seems to be more about the natural order of things, and for that line specifically, hope. I could be wrong about it, but I'm a lot more certain of the moon's broader significance.
Because it's fairly easy to line the moon up with hope and unity. The moon follows Ruby around in the Red trailer like her personal hype man, and every trailer has a shot where the girl in focus is framed by the moon right before striking an enemy from above. (except Yellow of course, but only because Yang was indoors) The moon shines silver, and I've already mentioned previously how I think that color relates symbolically, in large part because of the tales of silver eyes. The moon is also a guiding light in the night (that's the relevance of the line from Path to Isolation) which is a pretty strong symbol of hope.
I feel certain there's more to my point, but I've been writing this for a couple hours now and it's gotten kind of late lol
I'd love to discuss this more! I hope this is all coherent and comes across well. I think there's a lot to explore with the moon's significance to RWBY as a whole. This is all I've got in me for the moment though, so this is me signing off for now!
I see your reasoning there
I still think there's a strong symbolic association - at least early on and at least visually - between Weiss and the Moon, but your interpretation is certainly a valid one too