Andy,
If the beams were attached directly to the hull you could get away with beams 50mm x 50mm with a 2mm wall.
As with the Glider in the attached pic. It is 13ft long and a similar all up sail area.

The 14ft Paper Tiger has 50x50mm beams with 3mm wall and 100sq ft mainsail.

Both boats have a min platform weight of 50kg.

Once you put your beams on posts you create a lot of problems that will add weight to the platform without much benefit. My personal view is you would be better saving the weight.

Then that is just my personal opinion.

Regards,
Phill