I know about this mostly from quite a few gifs with the phrase "Let Me Love You". Frequently, these are when someone is chasing someone else.
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Edit: There's many more I would post, but right now embedding and changing the size seems to cut off the rest of the post
As for origin… I'm unsure.
I know various songs have had this as part of their Lyrics/ Title.
There's one song by Da Buzz: "Let Me Love You" from 2000, but it didn't seem to get big outside of Sweden. Mario's "Let Me Love You" from 2004 is much more well known (one video has +39 million views.) There's also Ne-Yo's "Let Me Love You (Until You Learn To Love Yourself)" from 2012 with +85 million views. That all having been said, I think that this phrase may not actually have any real association with those songs, just having the same phrase by coincidence. Also, from what I've seen, the popular use of it on the internet predated Ne-Yo's song
I know the tag "let me love you" is used for things that are not actually on these kind of images or the songs on Tumblr at least, for things I assume the user actually loves. The same goes for Twitter, which seemed to start becoming a hashtag unrelated to the songs in 2010.
The Google Trend peaks at March 2005, but I think that it may be due to Mario's song. The other peak I think is likely due to Ne-Yo's.
What do you guys think?