It's actually saturated fat in the diet, not dietary cholesterol, that raises your blood cholesterol. You don't need to worry about dietary cholesterol intake. Saying that, the yolk does contain some saturated fat, so I Wouldn't eat like 24 yolks in a week, but 2 whole eggs a week - you could eat 2 whole eggs a day and be in the clear.
IF you're trying to lose weight, you need to burn more calories than you're consuming, and the best way to do that is to track calories and know your intake, so you can control it. Eggs are about 50-70kcal per egg, so 2 a day is perfectly fine I think. The white on its own has significantly fewer calories though, only bout 20kcal per egg white.