I'm not sure what you mean. Deadweight loss is tautological. Maybe you're asking for evidence that taxes distort markets? If you accept that as true it's easy to see that deadweight loss is just the difference in surplus before and after the tax. Every econ paper on tax policy will try to measure the deadweight loss of the intervention.

I guess I just find it weird to have a page on Wikipedia about a quantity with no mention of what that quantity has ever been measured to be?

Wikipedia is a very difficult way to learn economics. In many ways it's like trying to learn mathematics or physics from an encyclopedia. The encyclopedic approach is - pedagogically speaking - sub-optimal.

But if I look at the page for "friction" it has tables of actual values and many references to practical experiments?

NB I was just comparing the writing style of that page (which seemed a bit odd to me) with other examples.

https://en.wikipedia.org/wiki/Friction