Why do my seedlings grow tall and floppy?
Tall, thin, pale seedlings that fall over are stretching toward light, a response called etiolation. The plant is investing everything in height to escape shade, at the expense of stem thickness and leaf development. It is almost always a light problem rather than a watering or feeding one.
A windowsill is usually insufficient, even one that feels bright. Human vision adapts so effectively that a room we perceive as well lit delivers a small fraction of outdoor light levels. A north-facing window in late winter, which is exactly when most seed sowing happens, is far too dim.
The fixes are straightforward. Give substantially more light, either from the brightest available window or from a grow light positioned close to the seedlings, typically within a few centimetres for a fluorescent or LED fixture and raised as they grow. Aim for fourteen to sixteen hours daily; seedlings also need a dark period, so continuous light is not better.
Rotate trays daily if the light comes from one side, or seedlings will lean.
Temperature contributes. Warmth speeds growth, and warm conditions combined with weak light produce the worst stretching. Once germinated, moving seedlings somewhere cooler and brighter than the germination spot produces sturdier plants.
Air movement genuinely helps. A gentle fan, or brushing your hand across the tops daily, stimulates thicker stems, the same mechanism that makes outdoor plants sturdier than sheltered ones.
Already-leggy seedlings can often be rescued. Many plants, tomatoes especially, root along a buried stem, so potting them deeper produces a strong plant. Others, including brassicas, can be potted slightly deeper but will not root from the stem, so improving conditions is the only option.