I was reading a book and a sentense goes this way..?

sizing someone up is normally when they are about to fight or argue to see if they can take them on, its to make a judgement call on if they can win, or if that persons not worth the time, or if they are too young.... its like the son , sized his dad up before he said he was staying out untill 11 pm . instead of 8 which the father wanted. kind of thing.

they checked each other out, usually how they physically look that is. It could also include sizing up what you can tell about their personality by looking at them as well. If there is a conversation between them that will also give you more information on the other person.

To size someone up is to figure him/her out. Decide whether the person is friendly/hostile, safe/dangerous, smart/dumb, honest/liar, etc. Prior to a fight it would be looking for strengths and weaknesses. Can I beat this guy? Should I run?

Each tried to form a judgment or opinion about the other based on what they could see at that moment.