what are the benefits/limits of constructing AEAD using Duplex mode with ARX primitive (chacha20 for example)? I understand that WAGE cipher uses duplex/sponge mode with stream based cipher for  Authenticated encryption with associated data (AEAD)  and NORX uses duplex/sponge mode with LRX structure , so , Is it possible to design AEAD cipher using duplex/sponge mode with ARX structure (Chacha20)? what are the advantages/disadvantages?

I could not find an example in NIST Lightweight candidates
It is possible!

The SPARKLE suite is a round 2 family of NIST candidates that uses ARX-based permutations to build sponge-based hash functions (called ESCH) and duplex-based AEAD (called Schwaemm): see their website and the NIST list of candidates.

Some advantages of ARX would be the smaller code size and the speed it allows. A disadvantages would be a harder masking (an implementation technique preventing side-channel attacks).