With the economy showing fresh signs of weakness, the measure advanced past a key hurdle on a 223-205 vote.
None of the men, in singles or doubles, advanced past the quarterfinals.
Does the underlined expression mean the same as "advanced beyond"? Can I use "overcome" instead?
Incidentally, I've just the thought that this might seem confusing because you've misunderstood the verb 'overcome'. When you overfill a tea-cup, the tea doesn't overcome the top, although it might be possible to say it 'comes over it' (although 'comes over' is more normally used of physical things: 'the soldiers came over the brow of the hill').
It would be more natural to say the cup 'overflowed'. To 'overcome' is to beat/vanquish/get the better of. And if the cup didn't quite overflow, the tea would 'come [right - optional-reinforcer] up to the top' The cup would be 'full to the brim'. I hope that isn't more information than you needed