The IWF has just released their decision on Russian athletes competing at Rio:

"The IWF Executive Board decided today to ban the Russian Weightlifting Federation from recommending/entering/participating with athletes and Technical Official at Rio Olympic Games 2016."

This decision is based on the McLaren Report and the IOC's decision to allow each sport's governing body to decide how to move forward with Russian athletes.

According to the IOC's guidelines on Russian athletes competing in Rio, the IWF removed six of Russia's eight weightlifters due to past doping violations or due to being directly implicated in the McLaren Report. The remaining two athletes were held accountable for Russia's doping scandal due to the new doping violations found in the reanalysis of samples from 2008 and 2012.

Further, the IWF has removed the Russian Technical Official from the Games as well, completely removing Russia from the 2016 Olympics. 

The spots that Russia had previously earned were redistributed. Algeria, Georgia, and Moldova each received one women's spot and Belgium, Croatia, El Salvador, Mongolia, and Serbia each received one men's spot.

Here's the full list of Russian athletes banned from Rio.