Hi Claire, I doubt it has anything to do with the bobbin tension, so please do not re-adjust it! If the bobbin tension was off, it would be off in both forwards and reverse. If it's only off in reverse, it's either a feeding issue or something with the check spring.
To explain: When you place a machine in reverse, the only thing that actually changes is the direction of the feed
dogs, which start going backwards. But both the upper tension mechanism and the bobbin tensions stay the same, they do not (and can not) themselves go backwards or do anything different than they do when the machine is set in the forward direction.
In other words, if the machine is stitching well in the forward motion, they ought to do the exact same in reverse--provided the reverse feeding motion is exactly the same. If it's not the same, it's possible your feed dogs are worn/blunt and only feed well in the forward direction; or that they are set too high or too low to gain proper purchase on the material in the reverse direction. If you look at the feed dog teeth, you'll see that they only "point" in one direction--in other words, they're not symmetrical front-to-back--which would explain why, if they're blunt, they won't feed exactly the same in forwards and reverse.
If you check the feed dog height and sharpness and they seem okay to you, the next area to look at would be the check spring. See if it has too much, or not enough, "snap" to it and adjust it accordingly.