Amazon Route53 Weighted DNS Routing

Here’s a good question someone raised that I can’t find an answer to-

If you were to use the weighted routing from Amazon’s Route53 DNS  to route users to two different versions of your website (Y and Z for example),  what happens when a user at home on a desktop computer  gets record set Z today and wants to go back to the site tomorrow, which record set will they get?  Y or Z?

What if the same user was at work and they got site Y? If they get Z again, great, but it’s not likely. If they get site Y they may have no idea what’s going on.

This is assuming the both sites are the same company but totally different versions which may or may not share the same back end/user database.

If it’s an ecomm site and they get X one day and Y another they may get totally different sites each time and not be able to complete a transaction or just as bad be terribly confused.

How can this situation be managed or said another way, how can someone who gets record set X always get it or get it for a specific period of time?

Or do I have it all wrong and this is more for load balancing than testing a new version of a site?

Make sense?