Hose Bib still leaks even after replacing washer
The term leaking is somewhat ambiguous, in that the hose bibb can leak at the stem or out the spout. Leaking at the stem is normally due to a worn or cracked washer, unless its quite old and that may require using "stem packing", namely a waxed cord material wrapped around the stem instead of a more modern washer. If the leak is more of a drip out of the spout it could be caused by a bad seat or worn stem that either will wear when over tightened.

Some bibs have a seat, normally brass, that can be removed with an Allen wrench, but most don't and may require the stem to be replaced. Most stems are pressed in past a bulge point that acts both as a safety feature, so that if you were working on the bib with the washer retainer nut off and loosened the stem where the threads were no longer engaged, the stem won't fly out under 100+ psi water pressure. So, if you fouled the seating area of the stem in most cases you can't get the stem out, your only real option at that point is spend the under $5 and replace the bib with a new one.