to be glad along with someone else about what they are doing, and so to approve of it or agree to it
This is the ordinary Greek word for being pleased with something, with "together with" fastened to the front, and that small addition does all the work. It never describes a private opinion held at a distance. It describes a person lining up their own pleasure with what somebody else is doing, so that the two of them now stand on the same side of the act.
Four of the six uses in the New Testament put that shared pleasure behind a killing, and the pattern is hard to miss.
- In Luke 11:48 Jesus tells the experts in the law that building fine tombs for the prophets puts them shoulder to shoulder with the ancestors who killed them.
- In Acts 8:1 Luke uses the word for Saul at Stephen's stoning, where Saul throws nothing and is still entirely with the men who do.
- In Acts 22:20 Paul quotes the same word back against himself years later, as something he did rather than something he merely allowed.
- In Romans 1:32 Paul makes it the last and heaviest item on his list: people who not only do such things but are glad when others do them.
The two uses in 1 Corinthians run in a gentler direction and show that the word is not tied to guilt. There an unbelieving husband or wife is content to go on living with a spouse who has become a Christian, and Paul tells the believer not to break the marriage up. The pleasure is quiet and domestic, but the idea underneath is the same: one person is willing to go along with the shape another person's life has taken.
The simple verb it is built on (εὐδοκέω) can stand alone, since God is well pleased with his Son and no second party is needed. Adding "together with" turns approval into company, which is why this word so often decides whether someone was a bystander or a participant.