Is it permissible to combine, when slaughtering a cow, the intention of Aqiqah for four people and the intention of Eid al-Adha sacrifice, and is there a specific weight for how it should be distributed?

It is permissible to share in the 'Aqiqah with a cow or a camel, and it suffices for seven if it is mature. It is also permissible to combine the intention of Udhiyah and 'Aqiqah in a cow. However, it is better not to combine the two intentions for those who are able.