Should I stick to the fork oil weight specified?
Rockshox recommends using 5wt in the upper and 15wt in the lower legs of the Reba, and differing the PSI to tailor for rider weight.  

140-160lbs = 90 - 105psi

160-180lbs = 105 - 120psi

180-200lbs = 120 - 135psi

200-220llbs = 135+

MAX PSI = 200

Although changing to heavier weights for heavier riders is not uncommon, i would stick with the recommended weight, especially if its working fine for you with tuning the rebound.

Sourced from the Sram 2014 Suspension fork air/oil charts