Cycle means feed from the magazine, fire, extract from the chamber, eject through the ejection port and push the slide back far enough to pick up the next round from the magazine and repeat all the above.
I wouldn't think a weak recoil spring would hinder the rearward movement of the slide. Allow the slide to move rearward quicker? Yes.
If I were you I'd unload the magazines, disassemble them, and clean them. The springs, the followers and the inside/outside of the magazine body itself.
Then, degrease the inside/outside of the magazine bodies and put some car wax on them. I used a cotton ball (pushed through with a pencil or clean wooden rod) to apply the wax to the interior of the magazine. You can apply it to the outside with a soft cotton cloth. Let it dry to a haze (just like when waxing a car) and then buff off the dried/excess wax with the soft cotton cloth. You can use the same pencil/wooden rod to work the soft cotton cloth through the interior of the magazine to remove the wax there.
Then I'd repeat the inside/outside waxing process, let them dry a few minutes, wipe the springs off with a lightly oiled cloth, put the maga zines back together and they should function better - if they are the cause of your problem. And the wax will smooth up the workings of the magazines and protect them very well from dirt/moisture. I waxed up some P01 magazines a couple months ago and they show no signs of rust/corrosion so far in spite of me sweating all over them everyday I'm working outside. I do wipe them off with a dry cloth/paper towel when I come in the house and they've stayed nice a shiny for two months now.
Along with servicing the magazines you need to field strip and clean the pistol and then lube it during reassembly. Then go to the range and see if it's working properly.
While some people report shooting hundreds or even thousands of rounds through their pistols/rifles/shotguns between cleanings you'll find some guns just need more cleaning/lubing. I had a buddy in college with a nice High Standard target .22 pistol. It would shoot one box of Eley match ammo just fine. Before the second box was finished he'd be taking it apart there on the range to wipe/brush it out and re-lube it in order to get it to function properly. I don't know if he ever shot it enough to "break it in" or not. I know it never loosened up in the couple of years we shot and hunted together.
Good luck with your pistol. I really like my CZ's. They are really good pistols.