I would think the red housewrap tape you can get at Home Depot would do the trick. It's light and I believe waterproof.

"This red tape is designed to be used for sealing seams and repairing cuts in housewraps, foamboards, poly barriers, and other types of exterior sheathing products. It is a thin, strong, polypropylene tape that is coated with a cold weather acrylic adhesive. It combines superior quick stick with excellent performance below freezing to -35°F (-37°C).
* Dimensions: 1 7/8 inches x 74 yards long
* Adhesion: 43 oz./inch width (12.0 N/2.5 cm)
* Tensile Strength: 20 lbs./inch width (90.6 N/2.5 cm)"
I imagine most of the brands have similar features. This picture and description came from
http://www.energyfederation.org/consumer/default.php/cPath/933_782
This tape is phenomenal for use to repair 3m Propore rain gear, like RainSheild. It stays on so well, that one can wash the coat in a washing machine and it stays on.
A lightweight way to carry some along is to wrap some of it around a one inch diameter pipe foam insulator wrapper which you can buy about a 4-6 feet section for under a dollar I believe at Home Depot as well. You can use another piece of the foam insulator wrapper, to wrap some duct tape around that.