Looking at the code of Weave the noweb option seems to be broken and deserted…
It just parses the document as markdown assuming different “noweb stule” delimiter for the julia code blocks.
This is an open bug: [BUG] texw example broken · Issue #412 · JunoLab/Weave.jl · GitHub
Seems that pinning Weave at 0.10.2 may be the solution until it is fixed.