There are a number of uses of dead weight but in your example it means that the professor was not moving or lifting himself at all. The author had to supply all of the force to lift him.

It's a noun. In your example 'dead weight' is someone not contributing. What they are not contributing to depends on context - usually they are not contributing to whatever group they belong to. Sometimes calling someone a 'dead weight' is slang for they are useless, stupid and good for nothing. But sometimes it is less negative and is simply saying they are not helping at all. "He's a real dead weight to society - contributes nothing." "We have 2 people in our work group and both of them are dead weights. They do nothing and just sit around." "My arm is not working, it's just a dead weight hanging down". ie My arm just feels like an inert heavy object that's not helping or contributing to anything. There's other meaning to dead weight as well: - weight of an inert non-helping object - ie animal laying down as if dead. - weight of an empty structure - ie metal crate -weight of cargo and passengers of a ship.

Yes it's a noun - weight is always a noun, you could see 'dead' as an adjective in this instance. Imagine a dead body or animal - the weight is very heavy without any help from the muscles of the person...