Does canonicity imply weak normalization?
Canonicity does not imply weak normalization. First, let me phrase the involved definitions more precisely:

WN: every open term is reducible to a normal term
Canonicity: every closed term is reducible to a canonical term

(Note: in modern metatheory of type theory, it is more common to talk about conversion instead of reduction, and likewise to talk about unique existence of normal forms instead of weak/strong normalization. This answer remains valid if we replace &quot;reducible&quot; above with &quot;convertible&quot;).
Normal and canonical terms are not the same. For example, the x variable in x : Bool context is normal but not canonical. Also, the closed term λ(b : Bool). if true then b else b is canonical but not normal.
Extensional type theory has the canonicity property but not WN, SN, or unique existence of normal forms. That's because in ETT it is possible to add an inconsistent definitional equality to the context, or add an equational theory of a Turing-complete system. For example, in the ETT context n : Nat, p : n = suc n the n variable has no unique normal form, since n can be expanded arbitrarily using p.
However, if we have a closed ETT term, we can't have anything dodgy in the context, so a closed term can be still evaluated to a canonical form.