Question
How far from the house foundation, and distance from a septic tank should a Weeping Willow Tree be planted?

Answer
Weeping Willows (roots and all) can grow extremely fast if given the proper nutrients and conditions for growth. They can grow up to several feet per year and will develop a spread equal to their height in many instances. They need to be spaced at least 40 ft apart. Their roots are highly invasive and will most definitely affect nearby water and sewer lines. The roots can exceed the growth of the expanse of the tree's branches by 3 to 4 times, so even planted a good distance away the roots are likely to eventually head toward your septic bed and clog it, unless you have a giant lot.
Many arborists don't recommend the Willow for residential lots due to its large, lateral size, messy habit of constantly dropping small branches and its invasive roots. If you want a "weeping" yard tree, cherry and birch species might be better options. Willows are better planted in their proper habitat along streams and ponds.
It's true that willow trees (and their roots) grow very rapidly. Their roots often wreak havoc when planted to close to sewer lines, septic tanks or drain field lines. A weeping willow grows to a spread of about 35 feet and their massive root system can be expected to spread AT LEAST that far. Because sewer lines provide the perfect growing conditions for these aggressive, water-seeking roots (loads of nutrients and moisture in an environment with a fairly constant temperature), they should never be planted anywhere near a septic system or drain field. All it takes is a hairline crack in your pipe, and the trees' tiny root tendrils will head toward this favorable environment.
This tree species grows fast and its roots are experts at seeking out water. The nutrient-rich water from leaky sewer pipes or cracked water lines acts like a magnet to the roots of these water-loving trees. This is why they don't belong in residential landscapes-not to mention that willows drop a lot of kindling and are quite messy as they age. It's hard to say whether or not your tree's roots will infiltrate your foundation, if they haven't already. One determining factor is where in relation to the location of your tree, that your water and sewer pipes enter and exit your home. As long as the roots have enough room to spread out, a solid structure like your foundation will divert the direction of their growth, providing that is, that any nearby pipes are in good repair and moisture doesn't tend to pool in the area. Build up the soil around your foundation and use rain gutters to divert the flow of water away from your home. If it doesn't impede the flow of water away from your foundation, you may also want to have a landscaper install a root barrier. Of course, prevention is the best medicine.