The words so as
(NIV: in this way) are not found in the original text. The grammatical construction Paul uses can express either result or purpose, meaning either In order to fill up the measure of their sins,
or As a result, they fill up the measure of their sins.
Although it is more common for Paul to use this construction to express purpose, it would make little sense for people to act in order to heap up their sins and bring wrath on themselves. Thus we should understand the sense here to be an expression of result: the result of opposing God and his messengers is that the Jews heap up their sins and bring wrath on themselves.1,2
Some commentators who opt for a purpose clause here recognize the difficulty of interpreting Paul to mean that Jews acted in order to bring wrath on themselves; accordingly, they interpret the meaning to be that Paul’s words are an expression of God’s purpose.3,4 This would be an unusual way of interpreting Paul, since there is nothing in the context to indicate that Paul had God’s purposes in mind; the focus throughout the section is on the actions and attitudes of the Jews.
16 by hindering us from speaking to the Gentiles that they might be saved so as always to fill up the measure of their sins. But wrath has come upon them at last!