If you want to delay an action within a hover, you can use javascripts .setTimeout() to add a delay of x seconds.
Try this, it will hide all odd items in a list, then add a hover effect to all the even ones, upon hovering it will instantly toggle the active class, and after two seconds it will toggle the next object:
$(".wypWedkarskie li").filter(":odd").hide().end().filter(":even").hover(
    function() {
        var obj = $(this);
        var nextObj = obj.next();
        obj.toggleClass("active");
        setTimeout(function() {
            nextObj.slideToggle();
        }, 2000);
    }
);
You can see a working demo here
Update :
This should give you what I believe you are after. 
It will highlight the item you are hovering over instantly. After 2 seconds, if you are still hovering it will show the 2nd item. As soon as you stop hovering it will hide the 2nd item. If you stop hovering before 2 seconds, the 2nd item won't be shown:
$(".wypWedkarskie li").filter(":odd").hide().end().filter(":even").hover(
    function() {
        var obj = $(this);
        var nextObj = obj.next();
        obj.addClass("active");
        setTimeout(function() {
            if (obj.hasClass('active')) {
                nextObj.slideDown();
            }
        }, 2000);
    },
    function() {
        var obj = $(this);
        var nextObj = obj.next();
        obj.removeClass('active');
        nextObj.slideUp();
    }
);
See a working demo here