What are some of the "thicker" decks?

Gwynydd

The Cathar is very thick
 

EricVolk

Tarot Illuminati is pretty darn thick.

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Denever

Kat Black's Golden and the Smith-Waite Centennial are nice and thick. The second edition of the World Spirit is a bit thinner and more flexible than the first, but the printing is better.
 

FLizarraga

The Vampire Tarot by Robert M. Place is almost unbelievably thick.
 

Debra

Egorov. It's lovely.
 

decan

The thickest deck I own is the Bonefire Tarot.
 

Citrin

Starchild Akashic
Lumina Tarot (at least the first edition)
Mary-El
Tarot of the Sidhe
Wild Unknown (first edition only, which is probably rare by now)
 

Nemia

Touchstone, too.
 

Eric in NJ

Nostradamus is painfully thick.

I wanted to +1 this and add that my Visconti-Sfzora replica (The Golden Tarot) has some serious weight to it.