Let me try to answer point by point -
1.I am looking for help in understanding why the size of the inbound WebSocket message is limited to 125 bytes.
It isn't, at least not by Tomcat.
2.The error that FF gives reads "The decoded text message was too big for the output buffer and the endpoint does not support partial messages" which to me reads like they are saying that Tomcat did not indicate during handshake that it accepts multi-part messages. True?
False. There is nothing in the handshake that allows one end not to support multi-part messages nor to limit the maximum message length.
That looks like a client side issue to me. Maybe you need to make the client side output buffer bigger.
Tomcat's web socket support (client and server) has been tested with the Autobahn testsuite that includes tests with significantly larger messages than 125 bytes both as single frames and as multiple frames.
3.The error that FF gives reads "The decoded text message was too big for the output buffer and the endpoint does not support partial messages" which to me reads like they are saying that Tomcat did not indicate during handshake that it accepts multi-part messages. True?
You are missing something. No idea what since you haven't provided any details of your client side implementation.