Why anomalous Zeeman effect is more common? Gone through many books, searched on Google, but couldn't find the answer.
The "anomalous" Zeeman effect is the name for the Zeeman effect with more than three - symmetrically distributed – sublines of the original lines.
Without the spin, one would expect 3 lines in the pattern only because the transition may change a single type of the spin $S$ only, by $\pm 1$, roughly speaking, from the spin of the photon. Quantum mechanically including the spin, there are transitions between many different states with various values of $L,S$ and other parts of the angular momentum, and they're allowed quantum mechanically as long as the total $J$ angular momentum is conserved.
One gets the "normal" Zeeman effect in the real world only for some simple – perhaps vanishing etc. – arrangements of $L,S$, which is rare, so most of the real-world Zeeman effects are those that were called "anomalous" because they couldn't have been explained without the spin.