Hi,
I've been on a tour of a Snake River hydroelectric dam, and the way the engineers' there talked about how much they monitior the AC signal it sounds like perfection is what they expect at all times.
As mentioned before, there could be a problem in your house mains connection. Some troubles there can result in low voltage in one circuit and high on the other.
However, I would much more expect that for the low cost irons it just "you get what you pay for." Manufacturing low cost products nowadays means quality just enough to last before you lose the receipt.
For the Weller iron, we don't know the history of the unit. Did you buy it brand new? Is it still under warranty? Even a good quality iron could need repairs at some point. And I think Weller does make some low-end units that likely are not made to the standard of their professional stations.
If you can swing it, a new Hakko or Weller station would most likely last a lifetime and you wouldn't have to buy another one again. My Hakko station is 10+ years old and still works like new (and has seen a lot of use).
Diagnosing the problems of your old irons. You might check if the heating element still gets hot, but not the tip? Then the problem is with the heat conduction to the tip and something may be loose or corroded there. Or if nothing gets hot at all, a wiring problem. I remember with my old 25W Radio Shack iron, the tip would get loose and stop heating. The tip was also not iron plated and would sometimes require filing the whole tip to re-expose pure copper again as corrosion would eventually wreck the tip. And replacements elements were available for those, so obviously sometimes the element would burn out (mine still works though).
73
Mark - N7EKU