Linen may just be the best sling fabric there is. Before cotton was widely cultivated, linen was the go-to fabric for just about everything -- daily wear, bedclothes, accessories... if it was sewn, it was made with linen. It's strong, supportive, long-wearing, and is especially terrific for hot climates, since the fibers tend to wick moisture away and allow it to evaporate, rather than holding it in place as a similar weight cotton tends to do. Soft but just slightly crisp when you first open the package, it gets softer with every wash cycle, so do wash before using it for the first time. Its reputation for wrinkles is deserved, but it can be smoothed out with a quick ironing if you're so inclined. I find it quite supportive in a single layer.
Age/weight range: Recommended from newborn to around 30 pounds. The fabric will certainly hold up to at least 35 pounds, but becomes less comfortable for long periods of time with increasing weights. I have used one with my three-year-old, who weighed about 32 pounds at the time, and it was fine for periods of up to 30 minutes, which is generally all a toddler will want for that up-and-down stage.