Wearing two suits causes more drag in the water, thereby making you feel lighter when it is time to race. We always called them drag suits - mostly older stretched out suits that fit loose, making more resistance.
I just found out first hand from a lady at my pool. Before I took my shower to get in the pool, she asked me if I noticed that my backside was totally see-through. I looked in the mirror with horror to see every nook and cranny through the old material. Since the front of the suit was still snug, I never noticed the backside. She mentioned that Latex suits wear out quickly in chlorine water. She was wearing two suits, both stressed out.
I chose to throw mine out and get a new one. If you are training, the two suit affect really drags and hangs off your body.
Coach and longtime swimmer here: both girls and boys tend to wear two suits at the competitive level. As one person hinted, one suit can appear a bit immodest at times. Latex suits do wear out quickly due to chlorine. Most guys, after they become comfortable or to penny-pinching, will start to wear a speedo and dragsuit (square leg oversuit made of a heavier material that doesn't thin). Girls don't really have that option so they wear two. It keeps everything very private, and does add a bit of resistance to make practice a little more challenging. Just think...when you swim 7.5k yards in a TOUGH practice with TWO suits on (one that's meant to drag), think of how much faster you'll be with ONE that is tight !!!