The weewx html page uses the pressure variable. That seems to display correctly. Though I played with it and tried changing pressure in the corrections section, and while that changes the weewx html page, it doesn't affect the weather underground one.
Changing barometer causes it WU change, but seems to work after the first update, but like I said, it changes the weather underground display once, then ignores it. EX: WU shows 30.00 inHg, I want it to show 30.10, so I do barometer + 0.1 in the conf, restart weewx, WU then shows 30.10 in as desired, but then 5 minutes later shows 30.00 again.
It's not a huge deal, just sort of weird that it works for 1 update period.
As for the model of the station, it's definitely an 01536 so I am not sure what the unit.