Some examples of the word's usage may be taken from the songs like 'Zara si dil mein de jagah tu' [give me a little space in your heart], 'zara zara touch me' [just, just touch me], 'zara dil ko thaam lo' [hold your heart for a moment] etc.
Zarra, or Zarraa, [Devnagari:ज़र्रा, Urdu:ذرّہ, pronunciation:Zarrā] however, is a different Urdu word with a double R sound, and means a particle, a speck, a shred. Zarraa is relatively less used, though it's a common word too.
One of the usage that I remember was in Noor from Delhi 6, which began with Zarre Zarre mein usee ka noor hai [There is His Light in every particle]. One recent song with the word in title was Zarra zarra mera de raha hai dua, by Sanjeev and Akshay Kohli, who are great composer Madan Mohan's son and grandson respectively.
One song where Zara and Zarra are often confused, is Tinka Tinka of Karam. The way Alisha sings it there, it sounds like 'zara' which means 'a little', but the context says the word should be 'zarra', a speck.