Dell recently came out with the Latitude E7270 series which seems ideal.
Small and lightweight, 14" or smaller, no more than 2224 grams
12,5" display, starts at 1260 grams.
Linux support (I don't mind if it comes with Windows but every hardware component should work well under Linux too.)
They come with Windows 7/10 but we have good experience running Linux on former dell Latitude models, so it's probably fine. (We have some issues with the Dell E-Port Replicators, kernel 4.5.3 freezes after docking while the notebook is sleeping.)
32GB RAM support
They have 6th generation Intel Core processor which supports 32 GB of memory. The notebook has two memory slots and 16 GB modules are available but Dell says that it supports only 16 GB memory (2x8GB).
Anyway, my E7270 (as well as my colleague's E7470) runs well with 32 GB memory. It has two 16 GB Kingston KCP421SD8/16 modules.
Can handle three external displays (Currently I have three displays, all of them has DVI input and VGA too, but I'd prefer the digital one. Using DisplayPort->DVI and/or HDMI->DVI conversion cables are also fine for me.)
6th generation Intel Core CPUs also support that and our Dell docking stations have three display outputs.
Faster than my current Intel Core i5-3230M CPU @ 2.60GHz
It can come with Intel Core i7-6600U which seems faster.
Anti Glare LCD seems fine.
Compatible with our Dell E-Port Replicators
It's compatible. The packaged Dell Docking Spacer for E7x40 is also handy.
Price on dell.com is between $1000-$2000.