My husband of 40 years passed away 11-12-13. He was 69. I was unaware of widows benefits and did not file until January 2016, shortly after I turned 61. I know I am receiving a higher benefit because I "waited" to file. If I agree to lower benefits and repayment of my overpayment can I retroactively collect benefits for the year I was eligible?
I'm sorry for your loss.
The answer to your question is no. Retroactivity is not permitted on applications for reduced widow's benefits, so the month in which you filed your application is the earliest month that you could choose to start your benefits.
You didn't ask, but if you are insured for Social Security benefits based on your own work record, you can apply for those benefits in the future if they are higher than your widow's benefit rate. If that's the case, it would probably be best for you to wait until age 70 to switch to your own record.