Why do larger alkyl groups show a greater inductive (+I) effect?
Qualitatively:

If a methyl group is more electron donating than a hydrogen, then an ethyl group would be more donating that a methyl group by the same reason.  

The effect drops off with distance, and generally a pentyl group is considered no more donating than a butyl group.

As for why a methyl group is more electron donating than a hydrogen, the carbon has a higher electronegativity than hydrogen (slightly), polarizing the bond (slightly).  This increased electron density near the carbon, which increases (slightly) its electron donation (I+) ability.