The whole mass of the Earth, mantle, crust, atmosphere and sea, contributes to the Earth's gravitational field, not just the core. Unless you want to split hairs, the Earth's gravity is the same now as it always was. In case you do want to split hairs, the Earth collects a substantial amount of space dust, meteorites and cosmic debris every year, but no one knows exactly how much except that compared to the total mass of the Earth the amount is negligible.
Estimates of annual accumulation vary tremendously, and leave out the contribution of mega-meteorites and asteroid impacts because they are not annual events. Remember that for every major impact on land, two hit the sea and are therefore not recorded. This accumulation increases the mass of the Earth and therefore its gravitational field, but it is balanced by loss of gases, mostly hydrogen, from the upper atmosphere. It is controversial whether losses exceed gains, but it is my view that when you take into consideration the contribution of major impacts, gains marginally exceed losses. Therefore the gravitational field is gradually increasing by an infinitesimal and unmeasurable amount as time goes by.
As for whether sea level was lower in ancient times, yes it was, but it depends on which ancient time you are referring to. In warmer times melt water from glaciers raised sea level, while in ice ages evaporation and precipitation lowered sea level and increased the ice sheet on land.