How to install kernel module updates?

I’m trying to install newly built kernel modules for an installed KMP package. The existing KMP package was not built to target my exact kernel version, so its installation created a “weak-updates” directory in /lib/modules/uname -r/.

After compiling the modules for my exact kernel version, I then moved them to /lib/modules/uname -r/updates and ran depmod, hoping that they take precedence over weak-updates. However, when I reboot the system, my new modules are not being loaded, even though I can manually insmod them (they work fine). How can I get the system to auto load the new modules on bootup?