I don’t think this is a stepper motor issue. My best guess is that you don’t have the vref set on your driver correctly and/or you have a mechanical issue.
Your stepper motor is rated at 83.6oz.in, which is a strong Nema17. It is stronger than the ones V1 sells. You can find Nema 17 motors with a holding torque of around 100oz.in, but that is only marginally better than what you have, and significantly more expensive.
The 2.77kg weight is only slightly higher than the weight of the common Makita rt0700 series router used on these machines. In addition, 2.77kg may be the package weight since this is only a 500W spindle.
There should be no issues using the spindle you have with the steppers you have. There are a lot of MPCNC builds with similar components that work just fine.
I’m assuming from the package that appeared when I searched for your board, that you are running DRV8825 stepper drivers. These drivers need to have their current set manually using the potentiometer on each board and a voltmeter. There are a number of tutorials (both written and video) on the web for adjusting the vref of the DRV8825. You want to be somewhat conservative in the setting since if you run your steppers near their limits, they may get too hot for the PLA plastic.
If your vref is set correctly, then I would next look to mechanical issues. Lubing and tightness might be the cause as Matt suggested. It is possible you have a loose grub screw on the connector between the stepper and the lead screw and what you are seeing is slipping rather than problems lifting.
There are a couple of low probability reasons for your problem. First, as Jeff suggested, it is possible you are driving the Z axis too fast. In order to determine if this is an issue, we would need 1) the first couple dozen lines of g-code of a file that has the issue with Z, and 2) know the type of lead screw you purchased. The lead screw will likely be either 1-start or 4-start. You can determine what you have by rotating your lead screw a single rotation and measuring how far it moves…8mm or 2mm.
If your machine happens to be a Lowrider, then how you wired the two Z motors may also be the root of your problem. If you wired them in parallel, you halved the Z torque.
Edit to add: If this is a vref issue, I suggest you start by setting the vref to 70% of max, which is 2A for tht stepper motor. If the vref is wrong for that driver, you need to check/set your other drivers as well.