Learn these transformerless power supply circuits, use a capacitor instead, it smaller and lighter than transformer. There are circuits as follows.
Reduce 12V battery to 6V for small circuit. You will love it same us.
First choice of Fixed Regulator using family IC-78xx. It is easy to use, cheap, popular for a long time.
The simple 6V Power supply circuit. We have a lot of circuits for you. Some ideas may be good for you. All circuits use normal component, easy making.