Just make a T-beam out of 2x6 or 2x8 (horizontal) and 2x4 (vertical) Douglas fir, waterproof polyurethane glue, and some deck screws. The vertical part of the T goes under the horizontal part and does not need to extend all the way to the ends. The screws are mostly just clamps to hold everything together while the glue dries. It'll last for years and if/when it rots, replace it with another for a just a few bucks. Doug fir is widely available, cheap, and nearly as light as spruce, but it's nearly as strong as oak and it lasts a long time in the elements.
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