The animations seem to look like they are playing at 30FPS even though I have 120FPS ingame.
It's most noticable on the players arms and weapon, any one know why?

Arms and weapon animations might be 30 FPS, though I am not so sure about that. As a 10 year old game, ETQW is not the first or last game that utilizes variable framerate for different entities. CSGO's weapon animations were too 30 FPS around 2014, no so sure about current status.
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Animations FPS was discussed here in a lengthy period of time, you check it:
https://forums.splashdamage.com/t/how-to-unlock-vehicle-framerate/139717
My config related with framerate as follows:
seta com_unlock_maxFPS "240"
seta com_unlock_timingMethod "1"
seta com_unlock_avgFrames "10"
seta com_unlockFPS "1"
seta r_threadedrenderer "2"
com_unlock_timingMethod is what changes animation FPS calculation methods; you can experiment between 0, 1, 2.

It has no noticable effect, thanks anyway.

I also tried this. No effect. Mouse aiming and static entities are 120+ fps, but aiming down the sights of the assault rifle still looks frustratingly choppy. The only solution I found was running the game on my laptop's built-in intel gpu, rather than my Nvidia 1050. BUT. Being a cheap built-in unit, it gets only about 15-20 fps, so that's a pretty frustrating trade-off.

It has no noticable effect, thanks anyway.
As I investigated a bit, com_unlock_timingMethod needs to be 0 in order to unlock animations' framerate.
seta com_unlock_timingMethod "0"
http://www.tweakguides.com/ETQW_9.html
Also, as these are video engine values, the game needs to be restarted to have the changes in effect. It is better to make those changes in etqwconfig.cfg at config directory:
https://pcgamingwiki.com/wiki/Enemy_Territory:_Quake_Wars#Configuration_file.28s.29_location
I also tried this. No effect. Mouse aiming and static entities are 120+ fps, but aiming down the sights of the assault rifle still looks frustratingly choppy.
That's weird. Frankly, aiming downside while using GDF infantry weapons is a bit disadvantageous due to the area covered by weapons and slight inconsistency of crosshair. Strogg doesn't have that since weapon model is hidden when player zooms in. Tourney mod solves that problem by hiding GDF weapon completely during aiming down the sights but that method applies only Tourney servers, not in vanilla servers.
If changing GPU fixes your problem, perhaps you should update your Nvidia graphics driver. As this is an OpenGL game, generic Windows drivers tend to suck comparing to Nvidia's up-to-date drivers.