The mean weight of a class of 34 students is 46.5 kg.

Mean weight of 34 students = 46.5 kg

Sum of the weights of 34 students $=(46.5 \times 34) \mathrm{kg}=1581 \mathrm{~kg}$

Increase in the mean weight when the weight of the teacher is included = 500 g = 0.5 kg
∴ New mean weight = (46.5 + 0.5) kg = 47 kg
Now,
Let the weight of the teacher be x kg.
Thus, we have:

$\frac{\text { Sum of the weights of } 34 \text { students }+\text { Weight of the teacher }}{35}=47$

$\Rightarrow \frac{1581+x}{35}=47$

$\Rightarrow 1581+x=1645$

$\Rightarrow x=64$

Therefore, the weight of the teacher is 64 kg.