Learn English – What does “put it down on me” mean

TheFreeDictionary defines it as:

To advance in a threatening manner: The ship bore down on our canoe.

There are many other meanings of the phrase, such as those given by Hellion, but this is the one I believe was intended.

"To throw down" means to fight someone (usually physical). It's a colloquial expression.

Interestingly, one entry on Urban Dictionary attributes its origin to "throwing down the gauntlet" an old tradition of throwing down ones gloves to challenge someone. The person challenging the other would throw down his glove or gauntlet, and the person accepting the challenge 'would take it up'.

You also see it used in popular culture like the TV show Throwdown with Bobby Flay, which is a show where Bobby Flay challenges people to cooking competitions.