The long and the short answer is, if you have seat assignments, which you indicated that you did. And the plane flies, you will be on it. I have never seen NW involuntarily bump anyone. IP is right in that there is generally no shortage of volunteers in the rare occasion that NW needs one. They are very good at load management and do not generally have oversold situations. Yes, they do oversell the plane, but at the gate, everyone that has a confirmed seat gets on the plane. I did get a bump about 3 years ago on a July 3 flight, and ended up going through MSP instead of MEM and got in earlier.
If your D/FW flight is weather delayed, than so will the DL and AA flights out of D/fw and no one will be jumping to other carriers. I live in D/fw also and generally the only weather delays here are afternoon thunderstorms which we haven't seen anytime recently.
I think you will be just fine.