My puzzle rating is 1770, and I expect that every puzzle I win gives me points but sometimes, it shows a check mark insteam of giving me rating
This mostly happens when it's a puzzle you already solved in the past or when the puzzle is rated too much below your puzzle rating (800 points or so).
It also happens when I set the difficulty to easiest.
That makes sense. IIRC the "easiest" setting should give you puzzles rated ~600 below your rating on average so that it's quite likely that some of them are rated low enough to give you no rating gain when solved. Or at least optically, the presented values are rounded to an integer but internally lichess counts with higher precision. Thus when your rating grows e.g. from 1792.78 to 1793.24, it looks as if nothing changed (still shown as 1793) but the actual value does grow.