>>17859673
They had a right to take what they were owed by force. That was standard for the times.
>>17859736
>He continued to pay them until he was deposed
No he didn't. He stopped the payments around November 1203 because the crusaders were contracted until March 1204. Alexios believed he could get away with not paying the full amount and that they would screw off when their contract expired.
>The Latins were there in the first place for completely cynical reasons and wanted to carve out Byzantium in the first place.
The crusaders wanted nothing more to receive what they were owed so that they can be on their way to Egypt. They never had any intention of conquering Constantinople until Alexios IV was murdered and replaced by Alexios V