The Groundhog (Deitsch: Grundsau, actually a "ground sow") bears some similarities to Ratatosk, the squirrel that runs up and down the World Tree, Yggdrasil, bringing news of the nine worlds.
While we have a Tree of Life (Lewesbaam) in Deitsch culture and in Urglaawe, our forebears saw similar imagery in other contexts as well, including the very land which they farmed. Groundhog burrows are often complex, with different rooms and multiple openings, all of which are used as allegories to the other realms of existence. The forebears thus set an analogy between the burrow and the Nine Worlds.
Thus, the Groundhog is the otherworldly messenger. The Groundhog brings news and prognostication from all of the visited realms. For an agricultural people, the short-term weather is naturally something that the people would like to know, which is probably why that particular feature was passed on to the wider American culture.
Within the Deitsch culture, the Groundhog Lodges often present other prognostications, sometimes presented in humorous contexts. Some farmers and some Hexerei practitioners observe the behavior of groundhogs and other animals at this time to make other determinations as well.
I am not so well versed in some of those, but one practitioner told me that the depth of, and the slope to, the first room in a groundhog burrow can serve as an indicator of wet or dry weather. If the first room is fairly close to the surface or is of a fairly steep slope, then the weather will be mostly dry. If the slope is not steep or if the room is higher than its entrance from the burrow, then one should expect wet weather. There are other behaviors that are examined as well.
Most historians will grant that Groundhog Day has its roots in heathen-era German practices, but the origins stretch back likely even further. Predicting weather or other things that can impact crops is a practice that transcends cultures, and observing the behavior of animals is an important tool in the forebears' kit. It was certainly not the only tool; lunar phases, historic weather patterns, river depths, etc., all were (and are) considered as well.
Remember that the events in Punxsutawney are not organic. We're not watching the behavior of a groundhog in the wild. Thus, what may seem to be a silly observance with frequent inaccuracies is not the whole of the story. The annual events in Punxsutawney (and other places) certainly helped to keep the essence of the lore alive, but the true significance of Groundhog Day is masked by the commercial pomp and circumstance of the day.
Groundhog Day is actually a visceral observance. It comes from a time when people had few reliable means of knowing when they could plant, and they relied upon their relationship with nature and with the animals to make determinations about the consumption of remaining food stores and to plan for the planting.
Thus, this weekend we shall honor the Groundhog and remember our interdependence on the animal kingdom around us.