[2+2 wannabe]

another way to look at it:

if the pot is large, and on the turn villain has a 1/5 chance of making his hand on the river to beat you. you have the option of either betting (charging his draw) or checking (not charging). assume that villain will always call your bet (as he has pot odds to do so).

if you bet, 4 out of 5 hands you will gain an extra turn big bet (as you will win 4/5 times) and 1 out of 5 you will lose one - for an expected value of 60% on your turn bet (you will win 3 total bets out of 5 wagered).

if you check, you gain nothing.

as you can see, betting gains more than not betting.