Suppose our utility function is the usual CRRA utility with $$\gamma=2$$ so that: $$u(C) = \frac{C^{1-\gamma}}{1-\gamma} = -\frac{1}{C}$$

Now suppose there are 2 goods, A and B, available for consumption. The consumption of A and B are denoted $$C_A, C_B$$. How do I compute the final utility?

For example, if I just add the utility, then the summed utility will be less than consuming either one of the goods, because the utility function is negative. $$u(C_A) + u(C_B) = -\frac{1}{C_A} -\frac{1}{C_B} < u(C_A), u(C_B)$$

Suppose also that we want to make good B "more valuable". ie. 1 unit of good B should be worth more than 1 unity of good C. How would I reflect this in the utility function? A simple scaling with a value greater than 1 won't work, again because of the negative utility: $$u(C_A) + u(C_B) = -\frac{1}{C_A} -k \cdot\frac{1}{C_B}$$ where $$k>1$$

For example the function $$v(C_A) = - \frac{1}{C_A},$$ and the function: $$u(C_A) + u(C_B) = - \frac{1}{C_A} - \frac{1}{C_B},$$ cannot simply be compared. The first represents preferences over one good, while the second gives preferences over two goods.
So if you say: $$u(C_A) + u(C_B) < v(C_A),$$ you are in fact comparing two different utility functions.
If you want to know what happens if you only consume one of the goods, you need to compare, for example $$u(C_A) + u(C_B)$$ with $$u(C_A) + u(0)$$.
Also if you increase $$k$$ in the function: $$-\frac{1}{C_A} - \frac{k}{C_B},$$ you are in fact making $$C_B$$ more valuable. To see this let's compute the marginal utility of $$C_B$$ relative to the marginal utility of $$C_A$$: $$\frac{MU_B}{MU_A} = \frac{\dfrac{k}{C_B^2}}{\dfrac{1}{C_A^2}} = k \frac{C_A^2}{C_B^2},$$ which does increase in $$k$$. So the higher $$k$$ the higher the value of an additional unit of $$B$$ compared to an additional unit of $$A$$.