Hi
I moved to the USA to marry my American fiance in 2007 and I had to show my fiance visa in my passport in order to marry. Maybe it's different in each state but here in the south, the waiver programme did not allow marriage.
You MOVED to the US to settle there once you were married which is WHY you had to get a Fiance visa for the US. It has nothing to do with which state because the state does not control Immigration to the US the Federal Government does.
If you had no intention of actually living in the US after you had gotten married then you would not have needed a Fiancee visa for the US, you could have entered, gotten married and returned to your home country on the VWP.
The OP wants to get married in the US, apply for a UK spouse visa and then settle in the UK. There is no need for the UK partner to get a US visa in order to marry and then return to the UK...they can enter the US on the VWP marry and then return to the UK no later than the 90 days allowed by the Immigration Officer when arriving on the VWP.