I don't think you are overreacting. Weakness is a common side effect of gabapentin.

I researched weakness extensively because i was weak for a long time. It turned out to be dangerously low blood pressure. Before that was identified, doctors kept trying to convince me to take antidepressants (which are the standard treatment for anxiety).

I've dealt with anxiety my whole life and know what's in my mind and body more than any doctor. People are arrogant to suggest otherwise.

Anyway, sometimes side effects flatten out and dissipate, so perhaps give it more time.