This is a very controversial topic and one well worth addressing since 40 weeks of pregnancy not only has a effect on the diver but also on the dive buddy. While there is limited research out on the effects of diving while pregnant, there also is not research saying that you should not do it. Sure we should all err on the side of caution but then you'd have to say pregnant women shouldn't ride a bike, drive a car, run marathons, lift heavy objects, etc. Just fifteen years ago women were told not to exercise or strength train because it could negatively effect the fetus. Now do to research and women not adhering to what was once the standard, we know that you can exercise but like everything else, there are parameters.
Studies done on sheep, dogs, and rats have shown that nitrogen does can cross through the placenta and into the tissues of the fetus. However, each species showed different results due to the placement of the placenta, number of sacs, etc. Yes, some showed damage to the fetus while others were perfectly fine. These animals were tested well beyond the typical limitations of what the recreational diver would go to. For example, 160 ft. for over an hour (simulation of course). There is no research that supports being pregnant increases your chances of developing DCI. One of the main concerns is that the nitrogen built up while diving will pass along to the fetus and but not be "breathed" off during off gas time.
While there are no studies with humans have been published since 1989 (no birth defects or abnormalities reported, BTW), surveys have been completed by women who dove while pregnant, some even into the third trimester. Survey results revealed that up to 5% gave birth to babies with birth defects or who later developed complications. The average rate of babies born with birth defects to women who do not dive is also 5%. So while the general consensus is to hang up the gear for 40 weeks, is it really necessary? I know plenty of women who dove while pregnant (not to mention the AMA divers in Japan) and gave birth to perfectly healthy babies. Another large concern is AGE's (arterial gas embolism) or gas bubbles. Fun fact, AGE's can also happen during sex when air is forced into the vagina and makes its way past the cervix and into the uterus....should we stop having sex when pregnant too???
Some things to consider if you do choose to dive while pregnant: make sure your gear still fits right, excess interstitial fluid may effect you ability to clear your ears, buoyancy may be off so be sure to adjust your weight properly, don't do any crazy technical diving you haven't done before, STAY WITHIN THE LIMITS, and allow some extra off gas time if you're really worried about it.
When doing your research, look for published, peer reviewed articles rather than just googling AND look at the date.....a lot of stuff floating around is from many many moons ago. The average person in general thinks diving itself is a VERY dangerous sport and would never do it, but we divers know the inherent risks, we educate ourselves, we have our gear serviced, and we don't do anything stupid (most of us!).