The lightest available harnesses all have a feature which almost eliminates their usefulness, IMO. They dispense with a buckled waistbelt whose size can be precisely adjusted, instead favoring either velcro or elastic to hold it in place, and the tie-in or biner to keep the two ends of the belt together when loaded. This is perhaps ok when the load comes from above, but there are many situations were the rope might be pulling toward your feet. In that case, the inability to perfectly fit the waistbelt above your hips via a tightened (usually double-backed) buckle may well result in the harness slipping off to your knees and beyond. These downward loading situations include: 1) Being the upslope person self-arresting to stop the slide of a rope team. Even with a tightened conventional harness, I've almost had it pulled off, having to stick my butt way up in the air to form a shelf for the back of the belt to catch on. (Stick your butt too far out and you may be levered off the slope over the pivot point of your feet.) 2) You invert, which is possible even in the the mild situations these harnesses were designed for. Such as while falling into a crevass on a glacier rope team. Or letting your feet get too far above you on rappel. Or in a leader fall, or possibly even when belayed from above, both of which can be happening during less-than-vertical scrambling or snow movement, which any harness should accomodate. 3) You do a hip or ice ax belay involving running the rope through a biner on your harness.
Harnesses that do not buckle include the 95 and older 130g CAMP XLHs, and the Cilao 100, 145 & 150g (three different models). While the weights are tempting, it would seem too easy to get into a situation for which they are not safe.
The harness I chose as my lightweight, not-hanging-around-much harness is the Mammut Alpine Light, 280g. It is essentially a slimmed-down BD Alpine Bod (395g) with a fancy Swiss weave that varies the belt width in different places. As a diaper-style, you can put it on around boots and skis, drop the leg loops while still tied in on the waist, and you don't have to worry about sizing leg holes. The light straps in back are dropable as well for dropping your drawers. (Several types of clips out there on the Alpine Light dropseat, some more useable than others.) It has two reasonably stiff gear loops.
Note that Mammut is updating this with a belay loop. This decreases multi-point loading on a biner, as well as the tighten-release feeling when the old style is lightly loaded, such as when walking on a rope team. The disadvantage is that you can't drop the leg loops and stay securely in the belt when changing pants or relieving oneself. It may be designed so you can chose not to pass the belt through the belay loop, but I haven't seen the new model up close to know if this is the case.
The lightest buckler is the 250g Trango Mountain Harness, which looks similar to the Mammut Alpine Light with belay loop.
Another light buckler is the Cassin Eolo, 260g (225g?) with a funky-looking set-up. (Might cause you to raise one leg a little when loaded, like a marionette.) Don't think it's widely available in US.
For light mountaineering, I've accessorized with 27g Mammut Moses wiregates (world's lightest by manufacturer specs) and Trango Superfly lockers 41g (likewise current lightest). Can still do a Munter on the little Trangos, at least with the 8mm rope I use in this role. I've slimmed down a notch to 5mm for prussik/belay escape/rappel backup/crevass rescue system loops. I use Mammut Contact 8mm single & double runners, 18 & 30g per loop, and a Petzl Tibloc on glacier.