As a general guide transport a/c are flown so that the wing is at or within reasonable proximity to the most efficient angle of attack.
For argument, consider that to be fixed. For all intents & purposes as weight increases then the speed needed to generate a sufficient amount of lift must also increase.
Starting at a particular height then the faster (ie heavier) a/c will require more distance to descend at the same rate of descent as the slower (lighter) a/c.