Concentrated Yerba Mate

You could do that, but it would not save much weight and will be perishable. The concentrate will have enough water to spoil. If you want to take this course still, prepare a concentrate by using about 4x as much mate and steeping somewhat longer. You can reduce it over low heat, but probably not enough to get a sludge without hurting the flavor.

If you're concerned about weight, I suggest light equipment. 50g of mate will make you about 15+ cups of it. To steep it, I suggest getting a very light tea infuser, either a basic basket or cup with built-in infuser. This way you can enjoy fresh yerba mate.

I have a feeling that you're going to be much better off with loose leaf tea here. Teavana claims that their mate tea is good for 25-30 t/2ozs or ~15 cups. Considering that you can brew it 2-3 times, you can get 30-45 cups of tea from 2oz of dry tea.

Condensing a Mate into a syrup you'd need to be able to concentrate it to the point of 1 oz making 45 cups of tea in order to get even an ounce of weight savings. That means that you'd have to condense ~300oz of liquid tea into a single ounce.

An alternative exists: simply buying ready-made instant yerba mate. It looks like this:

As you can probably see, it's a fine powder, a teaspoon's worth is about equivalent to a fresh gourd fill - so, it's quite efficient for when you're on the go.

Do note that:

• the powder is indeed fine and very sticky, so you have to take care when preparing your brew (e.g. when backpacking, shield yourself from the wind). Otherwise, it might get everywhere.
• the taste is somewhat different from "real" yerba mate (I would say not as good, but passable).
• the powdered form contains a quite substantial amount of caffeine per teaspoon (about comparable to a typical energy drink can). While nearly not as dangerous as pure, powdered caffeine, you should still be mindful of the dosage.

As a bonus, after you're done backpacking, a small amount blends surprisingly well with vodka (but recall the caffeine dosage note above)!