Is it safe to sleep on my back in pregnancy?

Sleep apnea. If you are a snorer and have gained a lot of weight with your pregnancy you may develop sleep apnea which may increase the risk of complications for you and your baby. Watch for that and inquire about it. Supine sleep may make any reflux symptoms worse.
Not after 16 weeks. You should not be flat on your back for prolonged periods. After about 16 weeks the uterus is large enough to impede blood flow in the inferior vena cava decreasing the cardiac output, which could potentially harm your fetus. You should sleep with a pillow or wedge under your right side to tip you to the left, or you should sleep turned well onto your right side.