Doesn't it switch on a per-request basis?
When a request makes it to Route 53, the weighting is applied every time.
Is the client machine's DNS cache functioning?
As mentioned, the request needs to make it to Route 53 in order for the weighting to be applied. If the record is being cached (client cache or resolver cache), the weighting will appear skewed because the request is being "answered" by the cache.
Am I correct in assuming that there is a 1/255 draw with one chance every 60 seconds for the DNS to be updated?
With a TTL of 60 and weighting of 1 and 255 respectively for two records, close. It will be a 1/256 chance to pull the record with weight of 1 and 255/256 for the record of weight 255  when the cache expires.
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