Did some number crunching comparing different tubes available in my neck of the woods.
Calculated deflections of a batten supported both ends with 5kg placed in the middle.
(Using formula from this site)
I realise a JR sail doesnt exert point load only at the centre of the battens, but this gives a comparison between different batten specs.

Alloy, temper, length, OD, Wall, weight - Deflection

6060 T5, 4.4m x 40mm x 1.6mm, 2.3kg - 36mm
6060 T5, 4.4m x 44mm x 1.6mm, 2.5kg - 27mm
6106 T6, 4.4m x 38.1mm x 2.0mm, 2.7kg - 35mm
6060 T5, 4.4m x 44mm x 3.0mm, 4.6kg - 16mm

The bottom one is the stiffest, best choice for upper battens.

But when you consider the yield stress of the T6 is ~ 210MPa and the T5 is only ~110MPa, that 38.1mm dia T6 tubing is almost the same "strength" as the bottom tube, just bendier.

The batten David Thatcher mentioned:
6060 T5, 6.5m x 63mm x 1.5mm, 5.1kg - 30mm
But because bigger sail area its more likely the loads would be bigger too, even if there are a couple more battens to share the load.

There's more on this topic in Bamboo and Aluminium Battens.

Arion has 38 x 3 mm alloy battens, 4.6m long, supporting a 35.7 sq m sail.  Robert Groves uses 25 x 3mm alloy tubular battens on Easy Go but once again I think his flat sail places lesser stress on his battens.  When my yard broke the top three battens bent.  The top, unsheeted batten bent the most and the third batten down also bent a lot.  For some reason the top sheeted batten, (second batten from the top) which also extends beyond the leech by 400mm, bent the least.  When I got into port I straightened them using the marina walkway railings as a fulcrum and was surprised by how much force was needed to bend them straight.  I think it is unlikely that these battens would bend under any circumstances other than yard failure, though I think a really good boltrope on the leech in particular and on the luff of the sail is important to spread the load in squalls.  I don't have any experience with wooden battens but Alan on Zebedee told me that if you can stop the top two battens breaking you wont break any others.  He made them heavier.  For a medium to heavy displacement cruising boat I think it makes sense to accept the weight penalty as a trade off against reliability.  It is also a relatively cheap solution and the components are easily repaired or replaced.  For performance cruising and racing, the criteria and therefor the solutions will be different.