It is actually quite common for a man who has been happily married to move on (and even re-marry) rather quickly after her death, especially if she has been ill. I don't think it is fair for anyone to judge him harshly for seeking some emotional support outside the marriage when a spouse is actively dying, because quite honestly, you have NO IDEA what you are talking about until you have been through it. It is also normal for someone with a dying spouse to begin their grieving before the spouse is gone.
Bewildered - I agree with indi that his mourning will likely take a lot longer than a few months. I grieved longer than that when I split with my first boyfriend of 5 years. However, I don't see any reason you shouldn't continue seeing this man. Just let him determine the pace, and if you grow impatient waiting for whatever you think you need, then you can move on.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?