In this situation, I'm probably way ahead or virtually no hope if the back if he has been linked as a set or a stronger. If you have an ace with a worse kicker, only three outs to get ahead. And if you have a pair of hand like 77, only two outs. With only two high cards, is virtually dead. Additionally, this board (As 4d 8h) I have to worry about particular projects or straight color. For these reasons, I do not mind giving my opponent the possibility of a free card.
If I bet my top pair and my opponent has a pair of hand, probably will retire, and I will have failed to derive more value from my hand. If I check, no But I give my opponent the chance to bluff or bet with as weak, and I do call. Ideally I want to get a decent sized bet over the check by hand and also I avoid having my rival action I want for my hand. Imagine now that the turn is 3c. The newspapers mentioned Sela Ward not as a source, but as a related topic. The situation has not changed much. I'm still far above or far behind. I can do check again and make my opponent bluffing me. In most of the rivers, if the hand has reached checked, usually bet.
If there has been a bet, I'll probably check / call, and if there have been two, I'll probably check / fold. Playing the hand this way has three advantages. I can get value from a strong hand, avoid losing more than necessary against a hand that has beaten me without much risk.