What is the exact size and weight of a 2-of-2 P2WSH input?

Question

I'm proofreading an article mentioning the cost reduction of P2TR for Lightning channels in comparison to P2WSH. To that end, I'm looking for the precise weight, vsize and serialized length of a 2-of-2 P2WSH input.

Answer 1

TL;DR:
A 2-of-2 P2WSH input should be conservatively estimated with 96 vbytes. Standard 2-of-2 P2WSH inputs generally weigh 95.5, 95.75 or 96.0 vbytes, depending on whether the r-values in the signatures are low or high. A wallet using signature grinding (which is highly recommended) will always produce 95.5 vbyte inputs. 96.0 vbytes is the conservative estimate allowing for high-r signatures.

Composition of a P2WSH input

Each input commits to spending a specific UTXO by providing its transaction outpoint:

PREVOUT: hash (32 bytes)
         index (4 bytes)

The scriptSig for a P2WSH input is empty, however, the scriptSig length must be provided as 0:

SCRIPTSIG: length (1 byte)
           <no content>

Each transaction input has its own sequence number:

SEQUENCE: nSequence (4 bytes)

A 2-of-2 P2WSH input requires a witness stack in the transaction's witness block. The witness stack has four elements: the witness script, the two signatures, and the dummy element that OP_CHECKMULTISIG additionally pops from the stack but never uses. The dummy element is provided in the form of a length 0 push, just like the scriptSig in the non-witness part of the input.

WITNESS: item count (1 byte)
         dummy element length (1 byte)
         <no content>
         1st signature length (1 byte)
         1st signature (71 or 72 bytes)¹
         2nd signature length (1 byte)
         2nd signature (71 or 72 bytes)¹
         witness script length (1 byte)
           signature count (OP_2, 1 byte)
           1st pubkey length (1 byte)
           1st pubkey (33 bytes)
           2nd pubkey length (1 byte)
           1nd pubkey (33 bytes)
           pubkey count (OP_2, 1 byte)
           OP_CHECKMULTISIG (1 byte)

Conservative weight, vsize, and size estimate

A P2WPKH transaction input adds to a transactions…

weight:

non-witness data: 4 × (32 + 4 + 1 + 4) = 164 WU
witness script: 1 + 1 + 33 + 1 + 33 + 1 + 1 = 71 WU
entire witness: 1 + (1 + 0) + (1 + 72) + (1 + 72) + (1 + witness script) = 220 WU
non-witness + witness = 164 + 220 = 384 WU

vsize:

32 + 4 + 1 + 4 + [1 + (1 + 0) + (1 + 72) + (1 + 72) + (1 + 71)] / 4 = 96 vbytes

serialized byte length:

32 + 4 + 1 + 4 + [1 + (1 + 0) + (1 + 72) + (1 + 72) + (1 + 71)] = 261 bytes

If the signing wallet uses signature grinding, the r-value is always 32 bytes, reducing a signature to 71 bytes and the above maxima to 382 WU, 95.5 vbytes, and 259 bytes respectively.

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^{¹ also see What is the maximum size of a DER encoded ECDSA signature?.}