If you are using proper technique... the differences in ease of manuevering would be minimal. If you are not using proper technique... you were probably straining/tweaking your knee... setting yourself up for an injury.
I would dump the money into physical therapy... with regularly strengthening and conditioning - you should be able to double the strength of your knee stabilizers... but if you were to buy the lightest board and bindings... at most you would probably drop the weight be 10-15%. I say this after having an ACL tear (someone crashed into my knee in ice hockey and 2 MCL tears (binding broke on a landing, crashed riding a chute and hit my knee on a rock spire).
agree with all above but i would add 2 points:
1) consider weight of the boot as well
2) I have a light board and bindings and a heavier board and bindings and I do notice it on the lift. I wouldn't sacrifice physio or gym membership for a lighter board but if you're not going to change your spending on those items a lighter board will at least make a difference on the chair, might mean an extra run or two per day. I doubt board weight will matter from a riding perspective in terms of strain on your leg, other than a light board might convince you to act like superman and thus hurt yourself.