Welcome to FlyerTalk! This is called back-to-back or nested ticketing and unfortunately it's specifically prohibited by Delta's contract of carriage -- rule 16c here:
https://www.delta.com/us/en/legal/co...f-carriage-dgr
That said if you do it once or twice, most likely nothing will happen. If you make a habit of it, Delta may take action against you, which could include such things as shutting down your SkyMiles account and voiding all your miles, and/or conceivably even trying to force you to pay the "avoided" fare.
If you have a long enough sequence of trips, you could do the same thing on multiple airlines with no problem -- book the "outside" trip on United, say, and then the "inside" trip(s) on Delta. But that can interfere with trying to earn status on a single airline, of course.
You could also extend one of your single-week trips to fly out on Saturday night, or come home the following Sunday, at the cost of a good chunk of your weekend. The trigger for the cheaper fares is usually whether the trip covers over a Saturday night. The value of that depends what these trips are for and who is paying.