I am looking for the first use of the term "deadweight loss." Any suggestions either as to who it was who first used it or how to search for it?
Start with Practical Points in the Formation and Valuation of Pension Funds, with a Note on Group Assurances Journal of the Institute of Actuaries July 1915. (alternative link):
...so that an unusually low mortality was a deadweight loss
The 1941 book The Cambridge Economic History of Europe from the Decline of the Roman Empire may have contributed to the use of the term, and says:
In addition there was the 'deadweight loss', the additional value that American users would have enjoyed had rails sold at the lower price and assuming that they would therefore have bought more than the 1,550,000 tons which they did buy...
So far as the "when" is concerned, Google Ngram can be helpful for this sort of question. It suggests (see here) that use of the term was nil or close to nil until 1960, since when its use has grown fairly steadily.