Summer weather is over for a couple of weeks; cool and showery today, even cooler Monday and Tuesday, then short break before another unseasonably cool rainstorm later in week; perhaps less unsettled and gradually turning warmer following week

Plain-language summary:

After summerlike weather for most of this week, it is much cooler today with scattered showers. It will turn even cooler and cloudier Monday into Tuesday, though rainfall will be minimal to light. It will be drier and a little warmer with a little more sunshine Wednesday before another storm brings more unseasonably cool and rainy weather later in the week, especially in southern areas. It will then likely finally turn less unsettled with more sunshine but still a bit cool for late May before possibly turning warmer towards the very end of May.

Meteorological discussion:

Much cooler and still showery today, even cooler Monday and Tuesday

After a somewhat summerlike week, widespread showers and thunderstorms yesterday, some of them severe with strong winds and large hail, much cooler air has moved in today, and summer weather will not return anytime soon. Now that the upper-level low is right over our region with cold air aloft, with lingering moisture and the coolest low-level air still lagging behind, there are still showers across the region with widespread cloudiness, though nowhere near as strong as yesterday's storms given the lack of instability. Cooler low-level northerly wind dominates Monday into Tuesday as the storm slowly pulls eastward, with the movement being slowed by the blocking pattern that has dominated North America this whole month so far. With widespread cloud cover and still a few showers, it will be unseasonably cool, with almost everywhere along and northwest of the Appalachians not getting above 55F (13C) on both days.

Source: TropicalTidbits

Still unseasonably cool for rest of week with another slow-moving storm bringing rain especially to southern areas, perhaps drier Wednesday and Thursday in northern areas

As that storm moves out completely and weakens by Tuesday night, yet another storm and closed upper-level low will be approaching in the Ohio Valley and move into the mid-Atlantic U.S. by Wednesday. At this point, it looks far enough south for our region to stay dry initially, with even peaks of sunshine at times, leading to slightly warmer but still cool (for late May) temperatures. The storm will likely strengthen along the U.S. East Coast on Thursday, akin to a winter Nor'easter, only this one will bring only rain and move much slower. After model disagreement over the past few days, most models agree today that the storm will track far enough south for the heaviest rain to only extend into southern Vermont to southern Maine, with progressively less rain farther north, fitting with the May pattern of southern areas being particularly wet. The storm will almost stall out and eventually occlude, leading to persistent rain through Friday and possibly even Saturday, mostly in southern areas, though lightening and becoming more scattered with time. The areas that see the steadiest and heaviest rain with thickest clouds may barely reach 50F (10C) for the high temperature, with areas to the north being somewhat warmer. Despite the unseasonably cool week ahead, the abundant cloud cover and low-level moisture will prevent a frost and freeze from occurring.

Source: TropicalTidbits

Likely stays cool for following week but perhaps less rain and more sun, then gradually warming up?

Next weekend, that storm should finally weaken and move eastward, but with the high-latitude blocking (-NAO) and then a western U.S. ridge developing (PNA rising though surprisingly not positive), continued upper-level troughing and at least weak cut-off lows will continue to influence our weather, leading to cooler than average temperatures and scattered showers, especially over higher terrain, though there should be at least intervals of sunshine on most days in the absence of a more organized, stronger storm. There are uncertain signs that the high-latitude blocking and upper-level troughing in eastern North America will slowly ease towards the end of May, possibly accompanied by a weakening of the western North American ridge, allowing for warmer, drier weather then, but this is too far out to have much confidence in any lasting pattern change.  

Source: TropicalTidbits

Source: Climate Prediction Center