Sforno on Leviticus 7:30/ספורנו על ויקרא ז׳:ל׳

1'ידיו תביאנה את אישי ה, seeing that the remainder of the animal belongs to the owners who had brought the offering, the owner together with the priest officiating on his behalf, presents this “waving” to G’d, this symbolic action indicating that basically the entire offering is G’d’s even if only the fat on the chest is offered on the altar, the chest itself belonging to the priest. The main reason for the “waving” is on account of that chest, to signal that actually it too belongs to G’d. There was no need to wave the fat, seeing we all know that the fat of every sacrificial animal always belongs to G’d via the altar on which it is burned up.