Well, what is 1/3 of a pound of butter? Butter producers try to make it reasonably easy for us in this country by splitting a pound into quarters and those quarters into 8 tablespoons. So a third of a pound (32 tablespoons) is 10-2/3 tablespoons (one stick, plus 2-2/3 tablespoons of a second), and half of that is 5-1/3 tablespoons (you’ll have to eyeball that third of a tablespoon).
If you have entered the new millennium* and purchased a kitchen scale, the math is as tricky, but one-third of 16 ounces is 5.33 ounces and half of that is 2.66 ounces. The real answer to your question is, a half of a third of a pound of butter is one-sixth of a pound. Neither a third of a pound nor a sixth of a pound is a very friendly amount to measure.
If you buy your butter by the pound, you could eyeball it and lop off a third of the block, then take half of that, and you’re likely to be close enough for the needs of most recipes.
While we’re on the subject, AMCO has a handy recipe divider with a huge magnet on the back, so that it will always be available stuck to your refrigerator. It helps you cut recipes in half and a third, and double or triple recipes. OK, it won’t have helped you, because it tracks measurements by volume (from 1/4 teaspoon to 1 cup or 1.25 milliliters to 237 milliliters), not by weight. And it’s not exactly rocket science, either, but we have found it helpful with the hardest part of dividing or multiplying recipes – remembering to divide or multiply EVERY ingredient.
*No offense meant, but it has been almost 10 years that we have been telling people that they will be better cooks if they invest in a kitchen scale. We have not changed our tune.