I Heart Chaos contemplates the difference:
Being a "Nerd" is now defined by having specific interests in something that is oddly specific, yet still currently accessible (i.e. the last three series of Dr. Who, or Star Wars) and is now desirable. On the other hand, being "Weird" is now defined by having extremely specific interests that most people still can’t relate to, or have no desire to relate to. These interests are so esoteric that they are actually more polarizing than desirable, so in other words, being weird is still undesirable, and if you’re weird, you’re still an outcast, which ultimately separates people who say things like "I’m such a nerd!" from true outcast weirdos.
The Dish 