Isn't the rise and fall of most of the large empires due to better weapons technology?

No; large empires generally collapse from within.

But Constantinople was by no means an empire when the Ottomans took it. By that point it had shrunk to a mere town.

Yeah, I guess I was thinking more "civilizations" than "empires".

I don't think so. One large factor in the decline of empires is when they get too big for the communications technology of the time to handle, i.e. if it takes too long for a message or an army to travel from one end o the empire to another.

The British, Spanish, French, Mongol, Ottoman and Roman empires all suffered from this, to some extent.

One reason the British Empire went down cause it became too difficult to sustain, both globally and internally

That was certainly the case with China.