Heathcliff has a brash, headstrong personality. As someone who's spent his time out in the Backstreets (for those unaware, it is basically the rough part of town), he has grown to be defensive, tempermental, and bold.

 For his voice, he should sound bold with a medium to low pitch and a gruffness that comes off as confident in himself. And, most importantly, he has a prominent British cockney accent.  Please make the British cockney accent. That's the most important part. :) 

Heathcliff voicelines/reference can be found here.