To find the total amount of nuts the chef bought, we need to add the weight of the almonds and the weight of the pecans together.
The weight of the almonds is 41.68 kilograms, and the weight of the pecans is 0.6 kilograms.
Now we perform the addition:
\[ 41.68 + 0.6 = 41.68 + 0.60 = 42.28 \]
Thus, the total weight of the nuts the chef bought is 42.28 kilograms.