Yes, you can always check if Weewx is running by regular rPi "status" command prompt, but is not a "monitoring" thing per say.
A nifty trick - which almost work as a "monitoring" - is to upload your wx data to WeatherCloud, WeatherCloud will notify you by email, if stop receiving your data... for weewx, rPi, network, or whatever would be. But you get notified to check on what is wrong... It saved me many times already... Xant -- You received this message because you are subscribed to the Google Groups "weewx-user" group. To unsubscribe from this group and stop receiving emails from it, send an email to weewx-user+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/weewx-user/2aaffd66-d864-482e-bc63-07afd7a786de%40googlegroups.com.