Dart

Big lump of code. I built a general slide function which ended up being tricksy in order to visit rocks in the correct order, but it works.

int hash(List> rocks) =>
    (rocks.map((e) => e.join('')).join('\n')).hashCode;

/// Slide rocks in the given (vert, horz) direction.
List> slide(List> rocks, (int, int) dir) {
  // Work out in which order to check rocks for most efficient movement.
  var rrange = 0.to(rocks.length);
  var crange = 0.to(rocks.first.length);
  var starts = [
    for (var r in (dir.$1 == 1) ? rrange.reversed : rrange)
      for (var c in ((dir.$2 == 1) ? crange.reversed : crange)
          .where((c) => rocks[r][c] == 'O'))
        (r, c)
  ];

  for (var (r, c) in starts) {
    var dest = (r, c);
    var next = (dest.$1 + dir.$1, dest.$2 + dir.$2);
    while (next.$1.between(0, rocks.length - 1) &&
        next.$2.between(0, rocks.first.length - 1) &&
        rocks[next.$1][next.$2] == '.') {
      dest = next;
      next = (dest.$1 + dir.$1, dest.$2 + dir.$2);
    }
    if (dest != (r, c)) {
      rocks[r][c] = '.';
      rocks[dest.$1][dest.$2] = 'O';
    }
  }
  return rocks;
}

List> oneCycle(List> rocks) =>
    [(-1, 0), (0, -1), (1, 0), (0, 1)].fold(rocks, (s, t) => slide(s, t));

spin(List> rocks, {int target = 1}) {
  var cycle = 1;
  var seen = {};
  while (cycle != target) {
    rocks = oneCycle(rocks);
    var h = hash(rocks);
    if (seen.containsKey(h)) {
      var diff = cycle - seen[h]!;
      var count = (target - cycle) ~/ diff;
      cycle += count * diff;
      seen = {};
    } else {
      seen[h] = cycle;
      cycle += 1;
    }
  }
  return weighting(rocks);
}

parse(List lines) => lines.map((e) => e.split('').toList()).toList();

weighting(List> rocks) => 0
    .to(rocks.length)
    .map((r) => rocks[r].count((e) => e == 'O') * (rocks.length - r))
    .sum;

part1(List lines) => weighting(slide(parse(lines), (-1, 0)));

part2(List lines) => spin(parse(lines), target: 1000000000);