Teapot, there is a scientific explanation which I'll reiterate but I also have a practical explanation.
In the past 6 years, I've been trying to lose weight off and on with visits to the gym and doing a mixture of weights and cardio. When I was on Jenny Craig, I dilligently did the program for a year along with going to the gym 5 days a week. I emphasized cardio with doing weights after my cardio workout. For the first 3 months, I lost 30 lbs, then nothing for 9 months. I tried changing up my workout program and even worked with the counselors at Jenny Craig but I couldn't break the plateau. Anyway, I gave up on diet/exercise for a while. Every time I went back, I did a similar thing where I'd exercise with cardio before weights and every time I hit a plateau around the same point (330 lbs).
It wasn't until this past year when I started reading more about weight lifting and such and started doing primarily weights and secondarily cardio. I lost 30 lbs before I did any cardio at all. I have shown more success in doing this than in doing what I did before and I've lost 50 lbs in about 4 months doing this, so I can testify that it has worked for me.
Now for the scientific reason. I may muck this up a little but I'll try my best. There are 3 sources of energy that your body stores ATP, glycogen and fat. We all know about the fat
ATP is burned really quickly early on in your workout. Your muscles depend on glycogen to help them lift weights and cardio can use either glycogen or fat, if glycogen is available it'll use that, otherwise it'll use fat. So if you do cardio before weights, then your body uses the glycogen which doesn't leave much energy for your body to lift the weights. If you do weights before cardio, then your body uses the glycogen for lifting and then uses the remaining glycogen and fat for cardio.
So basically in my personal experience, I know I am exhausted after doing a weight workout and it takes a lot for me to do cardio, but if I do cardio before hand then I just can't do weights as well. Your other option is to alternate days that you do cardio and weights.