[Samsung Gear 2] ST3ALTHPSYCH0:
It's actually in my last post. I've not found the weather apk, but I use that on occasion, so I'm not really looking to remove it. For Wellness (and other system apps) you'll need adb and samsung adb drivers.

Once you have those, connect the watch (the ROM has ADB over usb already enabled), open a command prompt in you adb directory, and input the following commands* :

adb start-server
adb devices (just to confirm that adb sees your watch)
adb remount +rw /system (this makes the /system partition read/write. This allows us to delete unwanted system apps)
adb shell rm /system/app/AsusWellness/AsusWellness.apk (This particular command deletes Asus Wellness)

*If you are on a *nix platform start each command with ./

I've assumed a Windows OS.​

I've also assumed that your watch is the only device attached in debugging mode. If not, you'll need to specify the device to adb.

Here's a list of system apps along with the associated files:

com.android.location.fused	/system/priv-app/FusedLocation/FusedLocation.apk
com.android.providers.download	/system/priv-app/DownloadProvider/DownloadProvider.apk
com.android.defcontainer	/system/priv-app/DefaultContainerService/DefaultContainerService.apk
com.android.providers.contacts	/system/priv-app/ContactsProvider/ContactsProvider.apk
com.google.android.apps.wearable.systemui	/system/priv-app/ClockworkSystemUI/ClockworkSystemUI.apk
com.google.android.apps.wearable.setup	/system/priv-app/ClockworkSetup/ClockworkSetup.apk
com.google.android.apps.wearable.settings	/system/priv-app/ClockworkSettings/ClockworkSettings.apk
com.google.android.apps.wearable.phone	/system/priv-app/ClockworkPhone/ClockworkPhone.apk
com.google.android.wearable.app	/system/priv-app/ClockworkHomeGoogle/ClockworkHomeGoogle.apk
com.google.android.apps.wearable.bugreportsender	/system/priv-app/ClockworkBugReportSender/ClockworkBugReportSender.apk
com.google.android.apps.wearable.bluetooth	/system/priv-app/ClockworkBluetooth/ClockworkBluetooth.apk
com.google.android.wearable.ambient	/system/priv-app/ClockworkAmbient/ClockworkAmbient.apk
com.android.providers.calendar	/system/priv-app/CalendarProvider/CalendarProvider.apk
com.android.backupconfirm	/system/priv-app/BackupRestoreConfirmation/BackupRestoreConfirmation.apk
com.asus.watchmanager	/system/priv-app/AsusWatchManagerWear/AsusWatchManagerWear.apk
com.asus.wear.watchinfoprovider	/system/priv-app/asuswatchinfoprovider/asuswatchinfoprovider.apk
android	/system/framework/framework-res.apk
com.android.providers.userdictionary	/system/app/UserDictionaryProvider/UserDictionaryProvider.apk
com.google.android.apps.translate	/system/app/TranslatePrebuiltWearable/TranslatePrebuiltWearable.apk
com.google.android.wearable.reminders	/system/app/RemindersPrebuiltWearable/RemindersPrebuiltWearable.apk
com.google.android.deskclock	/system/app/PrebuiltDeskClockMicroApp/PrebuiltDeskClockMicroApp.apk
org.esolutions.irremote	/system/app/org.esolutions.irremote-1/base.apk
com.android.keychain	/system/app/KeyChain/KeyChain.apk
com.google.android.tts	/system/app/GoogleTTSPrebuiltWearable/GoogleTTSPrebuiltWearable.apk
com.google.android.apps.fitness	/system/app/FitnessPrebuiltWearable/FitnessPrebuiltWearable.apk
com.xda.biktor_gj.gearsettings	/system/app/com.xda.biktor_gj.gearsettings-1/base.apk
ClockworkPhotosWatchFace	/system/app/ClockworkPhotosWatchFace/ClockworkPhotosWatchFace.apk
com.google.android.wearable.frameworkpackagestubs	/system/app/ClockworkFrameworkPackageStubs/ClockworkFrameworkPackageStubs.apk
com.android.certinstaller	/system/app/CertInstaller/CertInstaller.apk
com.android.bluetooth	/system/app/Bluetooth/Bluetooth.apk
com.asus.wellness	/system/app/AsusWellness/AsusWellness.apk
com.asus.tdc.s_mmi	/system/app/AsusSmmiTest/AsusSmmiTest.apk

You can use this method to remove any of these apks, but I've only tested the 4 I've mentioned. On the plus side, if you remove anything that's needed, you can always just reflash the Odin image.