How did “tight as Dick’s hatband” originate?

The Dick in this expression is supposed to refer to Richard Cromwell, son of Oliver Cromwell, the Protector. Richard unsuccessfully attempted to carry on the work of his father. He was ridiculed as King Dick and the British crown was called Dick’s hatband. But the hatband proved too tight for him to wear with safety and he threw up the job and escaped to the Continent, where he lived for many years under an assumed name. The phrase queer as Dick’s hatband is also supposed to allude to Richard Cromwell, who found the crown unsuitable for his style of head. One version of the saying is, “as queer as Dick’s hatband that went nine times round and wouldn’t meet.” Th.e second Cromwell was also known as Tumble-down Dick.