Rob Kardashian Into Sizzurp & Weed... DEEP -- Family Pushing for Rehab

Rob Kardashian's family wants Rob to get help for what they say is a very bad drug problem ... sources directly connected with the family tell TMZ.

Our sources say the family is well aware of what has been going on with Rob, depicted by these photos during a drug-fueled party a few days ago.

You can see Rob holding a double cup ... the container of choice for Sizzurp. The cup on the table actually has the words, "Codeine Boys" emblazoned on it. He's also seen smoking weed.

We're told the Kardashians have been calling rehab facilities, but Rob refuses to go. They feel desperate because they don't know what to do and hope pictures like these may change Rob's mind.