I've tried looking for this information on UESP and the Wikia but couldn't find where the Weir Gate to the Battlespire is located? Has it ever been mentioned exactly where the gate was?

Funny, I was just reading about Battlespire today. I'll have to look, see if there is anything. Part of me doubts it, but I will still look.

Also, don't use the Wikia. It's not reliable.

Hmmmm.... I found it to sometimes have slightly more information than UESP, but then also I found that UESP sometimes has more than the Wikia. I prefer UESP overall, although and I always go to it first before anything else.

If the wiki got more information, it's because they made it up.
Never trust them if it comes down to lore.

Sorry Dark, but UESP and TIL aren't bringing anything up.

Perhaps we could speculate on the location?

Part of that problem may be because anyone can edit it which means vandalism and trolls. I prefer UESP and use that. Love the layout and they've been around since 1995 or at least that's what their main page says.