Nice question.
When we speak of "bond strength" we are referring to the energy required to break the bond and leave each atom with one electron each. So the bond strength depends on the energy required to break it, which in turn depends upon the stability of the products. The stability of the products depends on several factors. For example, the C-O bond is stronger than C-N because when the C-N bond breaks the result is a nitrogen atom with a half-filled p-orbital. Since an O atom has more than half filled it is relatively less stable than N in this respect.
Now, a double bond like C=O would need to go through 2 successive breaks. In the first, the pi-bond breaks, resulting in a diradical. One elctron goes to C; the other to O. But we know that the bond was polarized--there was more electron density near the O than the C. This is for a good reason: the O has a higher effective nuclear charge than C, so the negative charge is stabilized by being closer to O. But now that the bond broke, leaving exactly equal electron density on O and C, the stability is gone.
Contrast that with a C=C bond. Since the electron density is equally shared between the 2 C's, there is no loss in stability in that respect since after the bond breaks the electron density is still equally distributed between them.
Hope that helps!