Top Heavy seedlings

Ive been having issues with top heavy seedlings wilting on me outdoors. Is this cause they are getting too much sun or what? Ive stopped using that miracle seed starter soil crap and went to peat moss pellets which seem to create a thicker stem. Seemed like i never had trouble when i didnt care as much. Now im over thinking i imagine. Can someone give me a play by play on seedling care for outside grow please? Ive germinated both from towel and straight soil so no problems there, its after that is my problem. thank you.

so...you're taking them from indoors to outside?...and transplanting to natural earth? ..or what?

starting them inside then putting them outside once they've sprouted.