Sea Star,
Pulau Weh is diveable all year around. According Lumba-lumba, if you are looking for calm seas on all sides of the island and sunny weather, then the months March, April, May and September & October are probably the best. November, December & January are the wettest.
We're there 3 weeks ago - we did not loose any dive but the sea a bit rough and the current was strong to fierce and unpredictable, particularly around the total eclipse. Still, you can find some easy divesites. My younger daughter; she did 10 bubble maker at shallows parts and very enjoyed the dive.
I'm too lazy to write a report but my daughters write something about the dive trips at their blogs, link below my signatures.
There's no direct flight from Singapore to B. Aceh - you've to KL and then by Air Asia or to Medan.
No visa on arrival facility at B. Aceh - get the visa before arrive or via medan.
Be carefull with AA, they cancel/delay our flight from KL to B.Aceh for one day. So, we loss one full dive day because of air asia.
Cheers
Wisnu