Great question. Staying level on your backswig is important as is maintaining the bend you create in your set up. Therefore, let's go to the source - your setup, and some great checkpoints.
The golf swing is a static dynamic movement. In other words, we start from a still position and then rotate during the swing. Therefore we need to be in a starting position pretty unique to this sport. We are not trying to move forward like in basketball, football, baseball or even tennis. Therefore when we set up with the weight totally on the balls of our feet (as we do in the above mentioned sports) we are set to use the incorrect muscles for a powerful , repetitive swing. This may be "heresy" but it is the truth. Watch the TOUR players and see how they seem more bent at the hips and their feet look firmly planted on the ground. Secondly, during ther swings they never move towards thier toes and rarely to you see a TOUR player lose his posture by raising up and losing the bend at the hips (his posture) through impact. Their posture doesn't change as many amateurs do.
So, to get in the correct set up, stand erect in front of a mirror with a side look. First see your earhole line up over your shoulder. That line should continue through your hip joints, knee and ankle joints. Keeping your head in line with your shoulders, begin bending at the hip joint where your legs fit into your hips. You can do this by placing your hands on your thighs and sense you are pushing your thigh bones (femurs) into your hamstrings. (Most golfers will bend at the waist). This will keep your tail bone (the only immobile part of your spine) in line with the rest of your spine all the way up to your head. Keep bending, with your knees locked until you are about to fall over on your heels, then let you knees bend slightly until the weight in your feet is 60% towards your heels (or behind your shoelaces) and 40% towards your toes. This then is your spine angle. To test if you are in the correct dynamic balanced position, attempt to lift one of your feet. This should be very difficult and feel like you need to move all your weight to opposite foot to achieve. You are now in your starting position.
That is a long way to go to get to your answer because now you can rotate from those back muscles and turn more level, balanced and set your backswing for a powerful downswing and strike on the ball.
A great drill: Take your new address postion near a wall where you can barely touch the wall with your right fingertips. Then put your right hand behind your back. Take your left arm with your palm facing skyward and rotate so that you can touch the wall with your left fingertips. This drill does a few things: 1) it teaches you to rotate properly (if you only use yoour arms int he backswing, sway, fall forward or reverse pivot on the backswing you cannot reach the wall); 2) enables you to see if you are staying "level" in your backswing and 3) show how the head actually moves during the back swing. Additionally it will provide a good stretch and sensation for the backswing.
Try the drill, fix your posture and balance and your game will come into balance and your shots will be better. Good Luck with it!