Well, besides the reasons mentioned above, lead is toxic, and although you do not risk to die when you touch it, it may cause some skin troubles if you wear the weight directly on your skin. Also you can inhale or swallow particles that may be released during the manipulation with the weight, or some particles can get into your blood through bruises on your skin.
And of course, it also dissolves to certain extent in water (that's the reason lead is no more used for cups as in the Roman times, or for plumbing like still a few decades ago). Well, "dissolves" is probably not the righ word - it is more that it mechanically and chemically reacts with water and other compounds in it, and gets ingested either as particles, or in chemical derivates.
In pools the raw lead lets traces on the floor, wall, etc - particles from it can then enter the bodies of visitors cutaneously, can be swallowed with water, ...
And at outdoors diving in fresh water, the next problem is that released or lost lead weight accumulates in the mud where fish, birds, and many other organism feed, and the lead can enter the food chain. It simply unnecessarily adds to the always higher level of heavy metals in living organisms, so it is better to limit the use of lead as much as possible. In France, (and probably in other EU lands) it becomes very difficult to find lead weights. The weights are now made of steel instead, and are hence also bigger. There is a EU law regulating quite strictly the manufacturing of lead weights, so I know that last year many store owners pre-stocked with lead weights, since it is almost impossible to get them now.
And there is another good reason for using coated weights - if you drop a belt, due to the flashy colors it is much easier finding it, than with a raw metal color.