Put a coffee filter into a medium metal strainer and set it over a bowl. Carefully spoon the yogurt into the filter evenly. Cover the yogurt tightly with plastic wrap, especially around the handle of the strainer. Put the bowl into the refrigerator for up to 8 hours (the "cook" time) to drain off the whey and thicken the yogurt. When the yogurt has drained to the thickness you like, continue the next steps.
Peel the cucumber, cut it in half lengthwise, and scrape out the seeds. Slice each cucumber half in half lengthwise and slice each into 1" pieces. Chop in a food processor, pulsing one second, stopping for two second, pulsing one second, stopping for two seconds until the cucumber is finely minced. Do not chop too long, or you'll have cucumber puree, which doesn't work in this recipe. If you don't have a food processor, finely mince the cucumber pieces. Place the minced cucumber onto a folded tea towel and squeeze hard to remove the liquid, which is discarded. Squeeze hard enough that the cucumber is almost dry. Set it aside.
Peel and finely mince the garlic. Finely chop the dill weed. Set both aside.
Have a medium glass mixing bowl ready. Discard the yogurt liquid. Leaving the yogurt in the coffee filter in the strainer, with a soft spatula, gently scrape the yogurt off the coffee filter into the bowl.
Add the cucumber, scraping it off the towel if necessary, sour cream, olive oil, lemon juice, garlic, dill weed, and salt. Stir well to combine.
Refrigerate for at least 1 hour. Will keep for up to a week stored in an air-tight container in the refrigerator.
Use as a sauce for gyros, Greek chicken, fried zucchini, fried eggplant, or as a dip for veggies or pita chips.