Why is my salted butter weeping? And is it safe to eat?
My initial guess was that there may be too much salt for the butter when it is at room temperature. However, 6-10% salt content is considered ideal with respect to curbing bacterial growth, as well as the retention and preserving the integrity of flavor. I highly doubt that your butter is salted to such a high degree that it would actually
Lacking further information, here are a few explanations

Precipitant from within, due to high buttermilk content: One purpose of salting is to remove buttermilk. Perhaps you are using a high buttermilk butter, and as salt facilitates the removal of buttermilk, if the butter was not properly worked relative to salt content you may be seeing either buttermilk or casein precipitant on the surface. Also, the buttermilk may not have been well washed out.
Precipitant from within, due to improper salt/water mixology: Salt should be worked into butter around 58'F, &quot;theoretically butter containing 15% of water should be able to dissolve 5.4% of salt&quot; (source). It is possible that (1) the temperature was not sufficiently high (i.e. to address addition of sea salt as opposed to table salt) to turn the salt into solution, or (2) the carrying capacity of the water was exceeded and salt crystals remained, or (3) the churning cycles were not sufficiently long to incorporate the crystals. These three things would contribute to higher reactivity in the butter than if it were properly dissolved. See explanation of Mottled Butter below for more info.
Precipitant from without, due to non-ideal elements in sea salt: Another explanation is that your sea salt had a high concentration of Calcium Chloride, which can attract water from the atmosphere to the surface of your butter.

Did you perhaps buy Mottled Butter;

Mottled butter is butter which is Uneven in color This unevenness in color may be due to several different causes. It may be due to specks of curd (speckled butter) and it may be due to certain organisms (dappled butter). These causes of mottled butter are not very common in factories where the manufacture of butter is properly carried on. The most common fault of mottled butter is the improper incorporation of salt and the presence of an excessive amount of buttermilk. Mottled butter caused in this way is common...
Whenever there is undissolved granular salt present the moisture is attracted and the color deepened at that particular place source

My guess based on the maount of information you gave about the butter (has sea salt, sweats at room temperature) is not that anyone of these answers is distinctly responsible, but that it is a confluence of the various factors resulting in a mild mottling (perhaps imperceptible to the eye or the palate unless you eat the whole block in one go) that is both attracting moisture from the air, and pressing it out of itself.
I am guessing that if you find the liquid problematic (i.e. does it have a funny taste/smell?) you can put it in the fridge and it will stop sweating/weeping. Otherwise, you run the standard risks of fats and proteins stored with a mild curing at room temperature.