Always buy weeks in advance.
Usually Airfare sales occur early in the week.
No evidence that Tuesday is the cheapest day to buy.
Domestic airfares change three times a day on weekdays and once a day on weekends.
What is true is Saturday is one of the cheapest days to fly. And Sunday is one of the most expensive days to fly.
Delta seems to be very consistent with its flights.
Generally, I will be looking at flights from Thursdays to Sundays or Thursdays to early monday mornings.
Delta seems to always offer these if buying around a month and a half in advance:
Thursday: Inbound: 3:30 PM - 5:27 PM and Sunday: Outbound: 6:30 pm - 8:40 pm. $166
Thursday: Inbound: 3:30 PM - 5:27 PM and Monday: Outbound: 6:30 am - 8:25 am. $156
Jet Blue seems to always offer these if buying around a month in advance: