2 people + 1 infant.
Well first I booked an international flight with United Airlines, arriving to India. They allow 2 checked bags. I think I have to pay a $200 fee to bring a 3rd. We came with 4, but, gotta throw one away. 🧳🗑

Now on a separate ticket, I'm booking a domestic flight. Air India Express or Indigo or Akasa air are my options, but Air India is the one that doesn't result in a long-layover, so I'll probably choose them.

So say we have 2 people and 3 checked bags of ~20kg each, then what's the fee?
Do any ICB (International Connecting Baggage) rates apply here, if it'll be on a separate ticket?
Do they use a total-weight or per-piece system? (e.g. Does it make a difference if we have like 15kg in 2 bags or 30kg in 1 bag?)

Air India Express | Products and Services

There you go

The fees are shown during the booking process, they will cluster the weight allowed for all pax and apply to whatever you check. Only Indigo gives an additional discount for international connecting baggage.

If I remember correctly, they have 3 difference baggage allowances depending on the ticket you purchase. Their basic ticket has no checked baggage allowance, the flex ticket has 15kg & the business ticket has 25kg.

I don't think you can check in a bag that weighs more than 25kg but they will be ok with you checking in 2 bags provided both combined are under the allowance. So basically in your situation, if you are 2 people with a total of 40kgs & buy the flex option then you will have to pay for an extra 10kgs. They do have an International Connecting Baggage rate which I believe is ₹3K for an extra 15kgs. So you can check in that 45kgs in 2 or 3 bags.