When do _WA_Sys_ statistics Get Updated?
SQL Server only automatically updates the statistics it uses. It may not be actively using the _WA_Sys statistics for cardinality estimation, though it may load them as part of the decision.

To see which statistics are being used for your query, add this to the end of your query, and look in the Messages tab:

OPTION(QUERYTRACEON 3604, QUERYTRACEON 2363);

If your database is in a compat level prior to 2014, you'll need these:

OPTION(QUERYTRACEON 3604, QUERYTRACEON 9292, QUERYTRACEON 9204);

These won't tell you why it's not using certain statistics, though generally if there are statistics created with a higher sampling percentage on the same column, statistics with lower sampling percentages will be disfavored.

Keep in mind that statistics updates don't occur on modification, only when queries run that use them