Weller WES51 transformer is a different bird at 40VA. Previously a custom Tyco part,
4000 series 4000-01E07G827, Tyco 2-1611453-5, Class II UL1585. Get this from Tyco:
"Inherently Energy Limited Transformers - Class II transformers up to 50 VA are “Inherently Limited” which means that the transformer, if overloaded,
will short itself out and fail safely, not requiring a fuse." 
Looking at IEC 61558 Transformer Safety, Part 15 on short-circuit testing and considering the WE1010 is almost twice the power 80-100VA would be a "non-inherently short-circuit proof transformer".
15.3.1 "The output terminals are short-circuited...."
15.3.2 "If protected by a fuse... the transformer is loaded for a time T and with a current equal to
k times the current marked on the transformer as the rated current of the protective fuse-
link, where k and T have the values shown in Table 4." {This is 1hr at 210% rated unless the polyfuse is easier}
The safety standard fails to say where the fuse is located- at the transformer input or output winding.
Secondary fuses are downstream of both windings, thereby useless at covering a transformer (winding) fault.
The safety standard fails to state where the output terminals are- before or after the Weller secondary fuse bodge?
It looks like a vague, poorly worded safety standard that can get exploited. Engineers have to let common sense prevail and "fuseless technology" would make most of us gasp.
If you want to see the hazard, run the station on 120VAC and short the transformer secondary or load it at max. power. Then grab a coffee.