Vertical Circles

In a vertical circle the weight always points down. With the direction toward the centre positive:

$$\text{top: } T + mg = \frac{mv^2}{r}, \qquad \text{bottom: } T - mg = \frac{mv^2}{r}$$

At the top both forces point to the centre; at the bottom the weight points away from it.

The string pulls hardest at the bottom. On a roller coaster the seat's normal force $N$ plays the part of $T$: at the bottom of a dip the rider feels heavier.