You should install them with the 3.75" side showing (standing on its narrow end) when you are looking horzonitally at the fence. If you install them the other way they WILL sag. I used to live in Texas and for some reason they were all installed that way, and every fence that had been up for more than about 6 months had a serious sag in the runners. The strongest setup for a 2x4 is for the 4" section to support the weight vertically. It is all about the section modulus, which is stonger when the vertical section supports the load. Just think about which way it is stiffer, common sense really.
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