Weisberger, the world number 38, struck 11 birdies in Malaysia to sit at the top of the leaderboard after day two.
Masters champion Willett, who carded a 67 on Friday to follow up an opening round of 66, looks in good shape in second place at the halfway stage, while American David Lipsky and Frenchman Mike Lorenzo-Vera are in a share of third.
James Morrison, Alexander Levy and Matteo Manassero all feature in the top 10 but first-round leader Marc Warren's 75 on Friday means he is now down in a share of 14th place.
Willett was particularly pleased with his round and says a more pro-active approach has helped him.
He said: "I holed a couple of nice putts when I needed to. I missed a couple of good chances too but if someone told me at the start of the day - five under, I would have bitten their hand off.
"I’ve just been committing to a few of the shots, it’s a relatively tight golf course on some of the holes if you want to take it on, so you just have to commit to a couple of the holes you like and hit good golf shots.
"I’ve not been necessarily perfect but if you’re trying to hit fade, they’ve got that look about them and if you’re trying to hit draw it’s the same thing."