My newly purchased plants don't have much for roots, should I:
a) leave the weights on and let them float
b) leave the weights on and plant them
c) remove weights and plant!
remove weights, plant. Sounds like they are bunch plants. They will develop roots soon enough. Prepare to find a couple floating at the top the first few days until they start to root. Just replant them when they do this.
If you want, you can leave the weights on until the plants develop roots. The weights won't do anything to the water and won't harm your fish (if you have any).
I usually do this so that the plants won't float. Once their roots are developed, you can remove the weights with no problems.