Know Your Meme explains:

Smoke Weed Everyday is a lyrical part from the 2000 rap single “The Next Episode”by hip hop artists and producers Dr. Dre and Snoop Dogg. The phrase has gained usage in numerious image macros, music remixes and YouTube Poop Music Videos .

Origin:

“The Next Episode” is a rap song by American rapper Dr. Dre featuring Snoop Dogg, Nate Dogg and Kurupt. It was originally released in October 1999 by Aftermath Entertainment as the lead single of his second studio album 2001. The song’s main sample incorporated David McCallum’s “The Edge.” Perhaps most notable for its open advocacy of marijuana consumption in the lyrics, the song received generally positive reviews from the music critics, who credited the album with rejuvenating the west coast gangster rap scene.

Meanwhile on YouTube, the closing line of The Next Episode, “smoke weed everyday”, became so recognizable that the song has been often referred to as “Smoke Weed Everyday”. There are several uploads of the song available on YouTube, with the earliest copy uploaded on June 6th, 2007. Another copy was uploaded on March 5th, 2009, erroneously credited as “Snoop Dogg ft. Dr. Dre – Smoke Weed Everyday”. The official music video of the song was uploaded via Dr. Dre’s VEVO channel on June 16th, 2009. The three versions have accrued 3.2 million views, 12.9 million views and 30.0 million views respectively as of June 19th, 2012.

On November 2nd, 2006, YouTuber ChubbyNipples posted a remix video containing the audiotrack from the 1996 Kirby’s Gourmet Race mini-game and Snoop Dogg’s 2004 rap single “Drop It Like It’s Hot”, which was taken directly from a YTMND site called “Snoop Dogg’s Dreamland (full song)” created on October 11th, 2006, by the user barf. As of April 2012, the video has accrued more than 2.7 million views on Youtube and 600.000 views on YTMND. Although not a Next Episode remix itself, this video did introduce the black and white GIF of Snoop Dogg jigging from side to side, which was directly taken from Pharrell Williams’ and Snoop Dogg’s 2004 music video for Drop It Like It’s Hot. 

The GIF can be regurarly found back in Next Episode remixes.

In November 2010, YouTuber irondadphazon posted the first unprofessional remix video titled “weed party”. Although not gaining many views, this and other similar videos he made did inspire other Youtube users to make their own YTPMVs of it. Unlike the Snoop Dogg GIF used in the remix videos, these YTPMVs mainly used a face shot of Snoop Dogg wearing a hood and holding a cigarette.

Then in July 2011, YouTuber Freuderthreep posted his remix video titled “SMOKE WEED SUPERSTAR – KINGDAYDAYDAY,” which combined Dr. Dre’s rap song with the background music theme from the Nintendo’s 1996 game Kirby Super Star. This video also returned the idea of using the GIF from the Gourmet Race remix.

The video was featured on The Mugen Fighters Guild Forum and within days, dozens of parodies and mashup songs began to emerge on YouTube. Similar to other pop culture remix series like The Fresh Prince, the song has been most prominently remixed with popular 8-bit videogame soundtracks.

And that's how a 15-year old meme is created (Snoop Dogg + Nate Dogg + Dr Dre) and then spreads (YouTube + gifs + remixes).

Rap Genius' explanation is a subset of the Know Your Meme description:

http://rapgenius.com/Dr-dre-the-next-episode-lyrics#note-40560

Way to lean in, Snoop Dogg.

With Rigby and Mordecai of Regular Show:

Snoop Dogg Last Supper gif:

http://pandawhale.com/post/39056/snoop-dogg-last-supper-gif-hd

"Drop It Like It's Hot" featured future Mr. Happy, Pharrell:

No wonder Pharrell is so happy!

There are MANY remixes of "Smoke Weed Everyday" on YouTube.

This one has 37 million views:

Rasmus Hedegaard Remix has 23 million views:

Alexander Bader mashes up the Rasmus Hedegaard Remix with Macklemore:

I found that on the Best of Bootie 2013 mashup album:

http://bootiemashup.com/bestofbootie2013/

Snoop Dogg nodding yes:

http://pandawhale.com/post/38234/snoop-dogg-nodding-yes-gif