I've been less-than-firm hand shaker and not from any timidity or deceitful character. I disagree with everything you wrote as it all goes against my 65 years of experience.
Yo, decimon—Please note the caveat in my post “in general”. There are always exceptions to almost everything. There are real reasons for a “weak” handshake. They include medical issues like arthritus or whatever.
I am curious though, why would one choose to shake hands weakly if it was not necessary due to some malady?