Something to point out and, hopefully, to be noted: bobbing and weaving is not a haphazard hit or miss endeavor. Rather it is something done deliberately and knowingly, with a definite purpose (ie, a specific punch) in mind. For example, the famous Dempsey Triples.
The first began by slipping inside an opponent's left jab and landing a straight right to the heart, then shifting the weight to the right leg (while stepping right and slightly forward with the right foot) to "bob" back under the left (while Dempsey hooked his left to the foe's body), thereby "weaving" to the outside position, shifting the weight to the right foot and throwing a right hook to the jaw.
The second was based off a slip to the outside of an opponent's left lead, dropping the weight to the rt foot and and hooking the left to the body, then stepping to the left with the left foot shifting weight to the left leg and , while "bobbing" back under his foe's left (and hooking the right to the heart), Dempsey would "weave" to the inside position and throw a left hook to the chin.
Point I'm trying to make is that you don't just "bob and weave". It is a series of planned motions for a specific purpose- avoiding his lead by slipping or ducking, then bobbing back under it and weaving your way to a more favorable position from which to land a punch. It is not something you do at random hoping he'll miss you and there is no point in being so low as to be unable to punch, no more than it makes sense to have your feet parallel or shoulders square while doing the "bob and weave". Also when weaving to the inside it often makes sense, depending on your plan (once you get there) to place a left glove over his right glove. So he can't hit you.