Possible causes of the putative rise (generally accepted as 4-8" in 150 years and accelerating in recent decades) include melting land ice, thermal expansion, groundwater pumping and an assortment of other notions.
Both the absolute “mean” rise and the contribution are the subject of a lot of research and papers, which is another way of saying that we don’t have a very good grasp. It is really really hard to measure “sea level” average. Most of papers on the relative contributions of various possible sources that I have seen are based on modeling, with parameterizations that, while not exactly WAGs, are at least estimates.
So, for example, one doesn’t have to look very far to find a paper which suggests that anthropogenic ground water removal and runoff along with other land-based water handling (perhaps closer to the OP’s question) contributed 42% (!) of the rise from 1961 to 2003.
“Model estimates of sea-level change due to anthropogenic impacts on terrestrial water storage”
Quote:
" We find that, together, unsustainable groundwater use, artificial reservoir water impoundment, climate-driven changes in terrestrial water storage and the loss of water from closed basins have contributed a sea-level rise of about 0.77 mm yr−1 between 1961 and 2003, about 42% of the observed sea-level rise. We note that, of these components, the unsustainable use of groundwater represents the largest contribution."
For a topic as topical as ACC, you are going to find a boatload of opinions, theories and models all neatly summarized into lay articles for public consumption within a general paradigm that anthropogenic forcings are changing sea level in a generally upward and dangerous direction, but underneath those marketing summaries, the actual science is not well settled. At all. One has to go beyond a headline of “Antarctic Ice Sheet Collapsing” to recognize that what the science says is that, based on surface fluctuations, there is a presumption that the grounding line for the ice sheet is advancing; based on modeling there is an assumption that warming of that particular ocean layer is responsible for the advance of the grounding line; based on analysis of solid surface under the ice sheet there are no retaining hills; based on the absence of retaining bumps, the ice sheet can advance more rapidly; based on modeling, the amount that will actually melt due to advancement over X period of time could in theory contribute X to sea level, all over the next 500-1000 years. But in today’s paradigm, “Collapsing Ice Sheet” gets a read and an advert click-through. Throw in a picture of a big crack in a big ice sheet (even if it has absolutely no historic context) and boom: winner headline.