"Can be programmed via arduino ide"

This limits you to a single architecture really, so no real answer except P1AM.

Though you can do 200 LED lights and 200 load cells with most PLCs, doesn't have to be an Arduino one. The others just run on ladder logic or Codesys rather than C++ programming. Honestly a normal PLC and ladder logic with the way modern analog works seems far, FAR easier to me to implement than bothering typing up all the code in C++ yourself. Most of the hardware interfacing stuff is handled for you automagically in a modern real PLC (Arduino isnt a real PLC in my opinion, its a single board computer)

The main part of the inputs for the load cells is that you need a load cell amplifier/transmitter of some sort. There are a few PLCs out there that have modules that can connect load cells directly but they are few and far between, most just are analog modules and they take an analog signal from a load cell amplifier. Load cell amplifiers for 200 units is where the real cost and complexity are going to come in. Then you just need a PLC that can handle 200 analog channels.

The LS Electric PLC has a load cell input module, but it is 2 inputs for $300. You would need 100 of these which would cost $30,000. It is cheaper to get the Laumas TLB4 load cell transmitter that will do 4 load cells for $300, but then need an analog module in the PLC as well. This would cost $18,770 to use 50 of the 4 channel units and 13 analog modules with 16 input channels through a Productivity 2000 PLC. A BRX PLC wont work because it cannot be expanded out to 13 modules, you would want to use P2000 here if you go with a ladder logic PLC.

Watch this video for some examples of how to do analog temperature inputs in a P2000 PLC:

https://www.youtube.com/watch?v=3iPt_8C7UhE

Load cells will be basically the same, as it would still just be an analog signal into the PLC, only measuring weight instead of temperature. They dont go over it in the video, but you can use a SCALE instruction to scale the "digital counts" to any specific unit of measure that you want, though the scaling is likely going to be done on the load cell transmitters. You can see in the video how easy it is to set up analog signals in a real PLC, now imagine how much C++ lines you would have to write out for 200 channels of inputs on an Arduino.

If you are using the HX711 I'm guessing this is a somewhat cost sensitive project, the HX711 is relatively low cost though 200 of them are going to add up. The HX711 uses a clocked serial output to communicate with the microcontroller, you are probably going to need multiplexers to get enough ports.

Since off hand I don't know of any commercial multiplexer cards that would be suitable for that many points (but that doesn't mean there aren't any) I might consider multiple Arduino Megas (which have a significant number of I/O points though a single one doesn't have anywhere near enough)