As mentioned, weaver II is VEY obsolete and probably unsafe at this point.
I don’t actually remember what was the default behavior at the time, but what I am seeing seems normal.
When the browser is large you see the desktop view with the full menu, and as the browser gets smaller, it automatically switches to the mobile view with a drop down menu.
But you should upgrade, read the full step by step on the guide article referenced and below
Converting a Weaver II (Pro) or Aspen site to Weaver Xtreme – Weaver Xtreme Guide (weavertheme.com)