You can buy vapuor barrier shirts from companies like 40 Below or RBH Designs that will stop sweat moving through your layers (the RBH vest is all VP), but these are designed more for extreme conditions then most people would need.
First off people who tell me that ‘they sweat like a pig’ tend to also be poor at understanding how to use their insulation properly, and have poor skills in dressing (I’m not saying you’re in this category). The problem often stems from too many layers and the wrong type of clothing. I’ve never been a big fan of straight fleece, and have always preferred pile style materials, as I think they just handle water better (there are loads of articles on this site about the subject). Also, I often see people just wearing too many clothes. As with my last blog post, to have a system that provides the greatest level of comfort over a broad range of temperatures and heat outputs you need:
A: A belay jacket system (a big synthetic jacket that goes on when you stop).
B: Medium weight windproof pile top for cold low energy movement (climbing, slow walking, very cold conditions). This should be designed to allow rapid dumping of heat through the side and front zippers.
C: Lightweight windproof layer(s) that work as above, but under the highest levels of heat production (somewhere between jogging and fast walking). This would be a good quality base layer (Brynje or merino) and a windproof (Pertex) or a thin softshell (Rab Vapourise, Buffalo Techlite etc).
With that kind of system, unless you have a medical problem, or just need to get a bit fitter, then you should be able to stay cooler and dryer.
If this doesn’t work then make sure your base layer will work even when it gets damp and will dry quickly and wick moisture away. If you look at my last blog post then I think Brynje would be ideal and has proved very effective during military testing (big packs, too many clothes, stop-start etc).
Also, try and keep your core cool by adjusting your warmth using head and hand gear. If you stop you just throw on your belay jacket, and any moisture held within your minimal layers will dry quickly.
The vapour barrier idea would ideally need to be applied directly to your first layer, as sweat build up in a windproof would mean your base would wet out, and you would still get some (reduced) chilling of the back, and also a general increase in wetness. Maybe I’m wrong, but I’d probably not go down this route.
The most practical solution would be to go for a thin softshell base layer (shelled micropile), and wear with alone whenever you can, and a medium weight pile softshell (Buffalo or Montane) when moving slowly, wearing it next to the skin. You could throw in a very light base layer for warm days, and perhaps carry a spare that you could change into once you reach your destination. Also avoid wearing a shell as much as possible, as a Pertex layer acts like blotting paper and will really wick moisture (something like a Montane Featherlite ultra gilet may work well over a light base layer.
Oh, and there’s always the nuclear option of a whole can of antiperspirant!