How can I strengthen my back to support the added baby weight?

The Crib Time exercise will strengthen your back and arms.

Stand in a partial lunge with the left foot in front. Lean forward slightly at the hips. Rotate your torso barely to the left, so that your right shoulder is a little in front of the left and let your arms hang straight down from your shoulders with the palms facing each other. Use a rowing motion to pull your elbows back and lift light weights (2 lbs) to the side of your ribcage 10x. Repeat with the right leg in front and left shoulder forward. Keep the natural arch in your lower back throughout the exercise.

Advanced: Do a full lunge as you lower the weights and come up as you row back.