If you're maintaining at 2000, don't drastically drop 800 in one go! Far too restrictive and will more than likely affect your adherence to your diet, possibly resulting in binge eating that pushes you far over what you would have eaten at a sensible deficit. If you're also looking after a baby and breastfeeding, dropping to 1200 calories is damn well irresponsible advice.
Try dropping 100 calories a day to start, and work from there. If you lose weight, stick with it until you don't, then drop another 100. You want to lose a bit at a time on the highest possible calories to avoid massive drops in energy and struggles with adhere, while also making sure you're fueling your weight training and recovery.
Lifting weights is good for building muscle, but isn't overly efficient at burning calories. You could try a couple of cardio sessions or upping your activity. Track your steps - whatever you're doing now, try adding an extra 1000 a day, and build up from there.
Small manageable steps over time, without anything drastic and unsustainable is the best way.
I'm currently losing weight on 2100 calories a day (although I am 5'11") while hitting 10000 steps a day, with 4 weight training sessions. Currently no time or energy to add in cardio but I'm happy enough - loosing 1lb a week and lost 4 stone in total so far - but look like I've lost much more due to my change in shape thanks to the weights. Keep preserving op. It's hard, but it's worth it, and strength training is one of the most beneficial things you can do for your health and longevity