Why is carbon monoxide a "weak" lewis base?
$\ce{CO}$ is usually considered a Lewis base, as the lone pair on carbon readily donates it's electrons, for example forming transition metal coordination complexes. Although oxygen is more electronegative than carbon, the carbon is more rich in electron density in the $\ce{CO}$ molecule as it basically has a full formal negative charge. Additionally, products formed by the carbon bonding to Lewis acids are much more favorable that products that would be formed by bonding to the oxygen atom.  

It is also possible for CO to act as a Lewis acid however. When acting as a ligand with certain low-valent transition metals, the metal can redistribute electron density back to the $\ce{CO}$ ligand in a process called back-donating. In this case the $\ce{CO}$ molecule accepts electrons via it's antibonding $\mathrm{\pi}$ orbitals, making it act as a Lewis acid.