That curvy back that you've noticed lately is a normal part of pregnancy. Pregnancy with singlets can cause postural or back curve changes, but more babies means more weight so women pregnant with multiples will likely notice changes earlier. The medical term for that curvy spine during pregnancy is lordosis.
You may be surprised to learn that your back curves forward to keep you and baby safe. As your belly grows your center of gravity is throw off. You are too heavy in the front and with no counterweight you could fall forward on your uterus later in the pregnancy.
Your body changes and modifies to redefine the center of gravity by moving the spine forward. With the spine shifted forward your center is now forward - accounting for the extra weight in the front. When the changes start occurring, you may notice lower back pain as do a minimum of 50% of pregnant women. Later in the pregnancy that number may be much higher than the estimated 50%, especially when baby "drops" into the birth canal.
How does the body change shape like that?
Relaxin is a hormone released during pregnancy that may trigger the spinal/center of gravity changes. There is no evidence that Relaxin works to loosen ligaments like other pregnancy hormones, but it may trigger the changes needed to shift the spine.
After pregnancy your body will gradually return to normal, including your spine. There is a chance your spine will resettle in a new place, but you will never realize the subtle change pregnancy left behind.