How much does sea level rise due to sediment deposition?
In a 1983 Journal of Geology paper by Milliman and Meade, "World-Wide Delivery of River Sediment to the Oceans" (link) it is estimated that the world's rivers carry about $13.5\times 10^9$ tonnes of sediment per year. If we assume an average density of $2.5~\rm{g/cm^3}$, this corresponds to a volume of 8.8 cubic kilometers. The total surface area of the world's oceans is 360 million square kilometers. This means that the sediment of the rivers contributes to a rise in sea level of 15 µm per year, or 1.5 mm per century.

The IPCC estimated in its fifth report that the average rate of sea level rise is about 3.2 mm per year. That means that about 0.5 % of that rise could be attributed to sediment. It is certainly not a major factor, but is non-zero all the same.