Given that the weights are normally distributed with mean \(\mu = 0.75\) kg and standard deviation \(\sigma\) kg, and 68% of the weights are less than 0.9 kg, we can use the standard normal distribution to find \(\sigma\).

The probability statement is:

\(P(X < 0.9) = P\left( Z < \frac{0.9 - 0.75}{\sigma} \right) = 0.68\)

From standard normal distribution tables, \(P(Z < 0.468) \approx 0.68\).

Thus, \(\frac{0.9 - 0.75}{\sigma} = 0.468\).

Solving for \(\sigma\):

\(\sigma = \frac{0.15}{0.468} \approx 0.3205\)

Therefore, the value of \(\sigma\) is approximately between 0.3205 and 0.3215.