the values picked up

Unfortunately you do not give any context. This is an error often made by people posting questions about English usage.

The phrase "picked up" can mean "increased".

The context is" As far as the next period (1996-2002) is concerned, it is clear that the average house prices shrank only in Tokyo (Japan) by 5 percent. In contrast the values picked up in the remainder of the cities."

In this case, then, "picked up" means "increased".

Is "collocated" some sort of obsessive used term by ESL teachers these days? I managed to get all through grammar school, high school and two universities--including a double major in history and English literature--and never once used the word collocate.

Is this a Chinese thing?

That's the funny thing about words, Set. They are used to describe certain events, certain situations and guess what, you haven't encountered all situations.

There are many words that you've never used and never will.

Try engaging your brain before you set your gums to flappin'.

collocate
(of words and phrases) to often be used together in a way that sounds correct to people who have spoken the language all their lives, but might not be expected from the meaning

by http://dictionary.cambridge.org/

Got it， man?