Have you tried "ultralite" mdf? Sometimes referred to as Chilean Ultralite? It is about the third the weight of regular MDF. Any type of MDF would need to be painted and the paint would also add to the weight.
What about 1/2" Coroplast? Completely weather resistant and available in Black, or any other color is paintable with a paint appropriate for plastics.
There is also Sintra, but at 1/2" it would be very expensive and also heavy.
Is there a Regal Plastics in your city? They have Coroplast and also other things that may work for you.
Rob is right -- 1/2" (10 mm) black Coroplast (fluted polypropylene) may be exactly what you need. Lightweight, non-hygroscopic, made for outdoor signage.
If your mention of painting is only to make it black, then you should just use black Coroplast. If you need to paint it for some other purpose, note that the plastic surface would be OK for some paints, but not as good as any porous material.