Semi-integral points of bounded height on toric varieties

We prove asymptotics for semi-integral points of bounded height on toric varieties. We verify the Manin-type conjecture of Pieropan, Smeets, Tanimoto and Várilly-Alvarado for smooth and certain singular toric orbifolds upon replacing the leading constant with the one predicted by Chow, Loughran, Takloo-Bighash and Tanimoto.