To evaluate which statement regarding ethyne is incorrect, it's necessary to review the characteristics of the chemical bonds in ethyne (acetylene, $$\mathrm{C_2H_2}$$) compared to ethene (ethylene, $$\mathrm{C_2H_4}$$).

Option A: The statement that the carbon-carbon bonds in ethyne are weaker than that in ethene is incorrect. In ethyne, the carbon-carbon triple bond is composed of one sigma ($\sigma$) bond and two pi ($\pi$) bonds. This configuration makes the triple bond in ethyne much stronger and shorter compared to the double bond in ethene, which consists of one $\sigma$ bond and one $\pi$ bond. Thus, the carbon-carbon bond in ethyne is actually stronger than that in ethene.

Option B: The statement that both carbons are sp hybridised in ethyne is correct. In ethyne, each carbon atom is bonded to the other carbon atom and a single hydrogen atom, necessitating the sp hybridisation to form a linear molecule with $180^\circ$ angles between the bonds.

Option C: The statement that the $$\mathrm{C-C}$$ bonds in ethyne are shorter than that in ethene is correct. The presence of a triple bond between the carbon atoms in ethyne results in a shorter bond length compared to the double-bonded carbons in ethene. This is because the additional pi bonds in a triple bond pull the carbon atoms closer together.

Option D: The statement that ethyne is linear is correct. Due to the sp hybridisation of carbon atoms in ethyne, the molecule adopts a linear geometry with bond angles of $180^\circ$.

Therefore, the incorrect statement regarding ethyne is Option A: The carbon-carbon bonds in ethyne are weaker than that in ethene.