How can I prevent my dining table from tilting?
If the base is hollow and open at the bottom, I would try making it slide around something heavy.  Make a concrete block or something that will fit fairly tightly inside the base.  Make it a bit shorter than the base to ensure the table goes all the way to the floor.

Then when you setup the table you sit the block on the floor, lift up the table and slide it down on the block.

If it fits nice and snuggly, pushing on the table will try to tip the block as well.

To me this sounds better than filling the base because eventually, someone is going to have to move that table.  It is going to be much easier to carry up a flight of stairs if you have 2 pieces - a large but relatively light table, and a heavy but small concrete block.  You might even make some handholds in the block to make it easier.