The standard 1000's shock spring is not heavier than the R6, nor are the two directly comparible. The R6 shock is shorter than the standard rear shock but has a heavier rate spring (550lbs-inch vs standard shock's 425lb spring). Shock length, spring rate and internal valving differences means a direct comparison between R6 and OEM shocks will be pointless. To emphasise this, the FZS600 has a shock whose length is within 5mm of the 1000's unit... but it has an 800lb spring fitted to it.
FWIW, I had a mid-range R2 Nitron shock & an R6 unit at the same time back in 2010 and there was no significant difference between the two. It's well worth persevering with the R6 shock, set up right they are as good as many expensive aftermarket designs.
FZS1000 has a 178mm / 7 inch springR6 has a 165mm / 6.5 inch spring.