What exactly happened at early things is sparsely recorded, if not to say for really earlier times wholly non-existent as traditional sources. Without written sources, things get complicated.
But we have hints. Among those is that for a medieval perspective this civilising tendency was apparently comparably late, and parallel in temporal development with the ...
After more research it appears, that weapons might have not been allowed in Norwegian Things (or at least Gulathing) at all and were only used as a way of showing agreement in Germanic tradition.