What causes the angle of a parallax to increase?
Imagine three space bodies A, B and C. The parallax angle at A, as observed from B and C, increases when the side BC is fixed and A moves closer to BC, and also, when A is fixed and BC widens.
A is a star. B and C are telescopes in two locations. If A is a nearer star, the parallax angle at A as observed from B and C will increase. For the same star A, if one telescope C is drawn far away from A, the parallax at A will increase.