Definitely use lighter materials if you plan to travel with it, and if you're building it must make sure you reinforce it more than a 'normal' build. Wood is heavy so try not to use so much of it. Aluminum siding, aluminum roofing, steel wall studs etc. are a great way to reduce weight. Also design the front of the Tiny House to be at least somewhat aerodynamic and pay more attention to waterproofing the front of it as well since it will see more water penetration from travelling.
