If it is separate tickets, then Air India will certainly stick to their own baggage limit for the domestic flights.

(Any sensible airline would).

BA will be very likely to NOT through check because separate tickets, and the onward flight is not with a oneworld airline.
(If it was a single ticket, then providing they have an interline agreement, they would. But it is not one ticket, and the nextflight is not oneworld).

It doesn't hurt to ask.

However, don't expect them to say yes. And if they do, certainly expect the most restrictive weight/item limit to apply.