First, a note on how weewxd works: the driver blocks, waiting for data to come in. The program cannot do anything while it is blocked. Once data comes in, then it can proceed, emit a LOOP packet, then the rest of the program can process it.
Your fileparse polling interval is 60 seconds. This means that it will sleep for 60 seconds before reading new data from the file. Nothing will happen until it wakes up.
Meanwhile, your archive interval is 60 seconds. This means weewxd will take whatever data has accumulated over the previous 60 seconds and use it to create an archive record.
With such a short archive interval and long LOOP polling interval, you can see how it's easy for the program to be sleeping, or have nothing available at the one minute mark.
Solution: if you can, have data available more frequently than once every 60 seconds. This would allow you to shorten the fileparse polling interval. If that's not possible, lengthen the archive interval to at least 5 minutes.
Best yet, do both.
As for the "429" error, this is happening because your system is trying to register too frequently. Almost all weewx stations do this because the default registration interval does not work well with the station registration. You can ignore it, or tell weewx to do the station registration less frequently. In weewx.conf:
[StdRESTful]
[[StationRegistry]]
register_this_station = false
post_interval = 86400
Station registration is working fine.
-tk