Well, I think Weigel is misconstruing the concern a bit in that tweet. It's not necessarily about swing voters, but about whether this does anything to the enthusiasm gap on the right, i.e. people who voted Trump in 2016 and might be just disillusioned enough not to vote at all in 2020.
If it doesn't have a substantial impact, great. The NRA's influence has been waning under mismanagement and bad PR for a few years now, so maybe it's not the third rail juggernaut it might have been at one time...but I definitely do not think it's unwarranted hand-wringing to wonder how much a case against the biggest 2A lobbying group there is might impact a national election that is less than 3 months away. Especially in this, of all years. Hope he's right, though.