Quite the carpenter! I'd be terrified to put a 1/2 ton of anything on something I built. Especially something glass filled with water and fish.
You could use wedges on either side. As long as the tips touching the frame on either side are on the same X axis of the main door pivot, the door will open fine. Or, the wedge on the left slightly behind the axis, and the wedge on the right slightly in front. But if they are exact, the door will open fine.
You can also put spacers on the tops and bottoms of each door to fill in all the gaps and make the whole shelf have an inset border.
This message brought to you from years of lego.
Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.