I don't have a WeatherLink IP.
However I have paid some attention in recent weeks, taking advantage of the fact I currently have two wireless VP2 consoles near each other in the same room, together with an Ambient Weather WS08 console.
With no logger installed (and obviously therefore no computer interaction) I had one of the consoles agreeing very closely with the WS08 in stable conditions (they differ in dynamic response, which is not the issue here).
Installing the logger complicates matters. Sadly it is not just a matter of a fixed added power dissipation at a fixed location inside the console. If it were an appropriate calibration offset in temperature could probably fix that almost perfectly, and a calibration offset for humidity could probably get close for the most common condition in my house.
However conditions of interaction with the PC by way of the logger produce time-varying temperature offsets (presumably because they induce time-varying power consumption changes, probably in the logger proper, and possibly in one or more of the other console components.).
A simple case in point of interest to me is that the seemingly simple interaction of the Cumulus program running on my PC transmitting a command to the console (by way of the logger), to update the console clock to agree with the PC clock gives a temperature spike in console-reported indoor temperature on the order of a couple of tenths of a degree. That does not sound like much, but given the thermal mass involved, and the short length of the interaction, probably means an appreciable excess power consumption is at hand.
More disturbingly I've seen several-hour offsets of more than a degree F for which I've not even been able to identify the inducing condition(s).
I think the console backlight temperature offset question gets more publicity here, but I suspect that one is a rather consistent power addition in a specific place, and so subject to successful remediation. The temperature offsets associated with PC interaction via the logger seem unlikely to be successfully addressed.
Maybe someday the fabled VP3 will do a much better job of isolating the console internal temperature sensor by some combination of location, insulation, and air flow channeling. Or maybe it will at least support the external temperature probe as currently do both the Envoy and the 8X Envoy.
Or maybe the particular ways that Cumulus interacts with the logger+console cause more of this trouble than do other possible ways, in which case Cumulus MX may already be better, and perhaps other programs as well.
None of which bears directly on the question posed at the top of this thread. But you'll realize that I'm not at all surprised to see a report of offsets attributed to WeatherLink IP. As it must burn much more power than must the basic logger just to do the job, I'd expect the offsets to be bigger. As I think I've seen over a degree, three or four is not implausible to me.