'Weigh the evidence' means to consider both sides of an argument, and to think about the many causes that provoked an event. It is a metaphor: 'weighing' literally means to measure the weight of something on a pair of scales-so 'weight' here is a metaphor for the 'value' of each side of the evidence. 'Pace event' must be wrong, as it does not make sense in English. Check where you found it again to make sure that it says that. It may be a typo. It is probably just an error, and is meant to say 'pace of events'. Pace is a noun, and means 'speed'. 'Pace of events' means how quickly a situation has come about: here the writer is suggesting that the situation in Syria was made worse because of foreign intervention, i.e. things got worse there much more quickly (pace) than would have happened had foreign powers not intervened.

"Weigh" here means to consider or judge the evidence, as to whether the evidence is valid or what exactly it means. I have not idea what a "pace event" is. Are you sure the original didn't say "peace events"?