Make sure your two quart jars (or half-gallon jar) are clean and sterilized — run them through the dishwasher and heat-dry before using.
Slice the cucumber and sweet onion. Layer them into your jar or jars.
On the stovetop in a saucepan, heat the granulated sugar, brown sugar, white vinegar, apple cider vinegar, salt, mustard seeds, celery seeds, and turmeric until the sugar dissolves.
Pour the vinegar mixture over the cucumbers and onions, filling to the top and completely covering them. If it does not cover, add a bit more apple cider vinegar or water.
Let the jar cool completely on the countertop. Then place a lid on the jar and refrigerate.