Both April and June are both transition months (weatherwise) in the Virginia Mountains. In early April, you would be right in the middle of transition from Winter to Spring. Consequently, you are quite likely to see a little bit of both if you hike during that time, and it would be imperative that you are prepared for both. If you are unlucky, you may experience some combination of bitter cold, high winds, heavy snow/ice or cool, damp fog, any of which can quickly lead to hypothermia if you are not fully prepared. On the other hand, if Mother Nature smiles on you, you can also experience some very nice weather with lots of sun, mild to warm days and cool evenings. Remember that weather at this time of year is very changeable. A beautiful, sunny, 75-degree afternoon can be followed by a stormy cold front passage, much lower temperatures and, then snow/ice all within a few hours and vice versa. Also, keep in mind that, as always but especially in springtime, elevation can make a large difference in weather conditions, and the trail in Virginia, especially southern Virginia, has some high elevations, including Mt. Rogers, which tops out at over 5000 feet, and a bunch of 4000+ foot peaks. The weather on these high peaks can be nasty even when weather in the valleys is quite benign.
June is also a transition month in the Virginia Mountains. The weather is changing from Spring to Summer, and, as such, it should not include the extremes of April. You may see anything from downright hot, humid mid-summer-like days to cool, rainy early spring-like days. Such cool rainy days are particularly troublesome because, if you are not careful, hypothermia can set in even when temps are in the 50s and 60s, especially if you are wet. Elevation will also impact weather in June. However, in my experience, it seems like the impact is only marginal on really hot days (when you’d love it to be substantially cooler) and rather more apparent on cooler (especially cloudy) days when temps can be quite a bit colder especially when you factor in the wind.
As for your question regarding other hikers, June seems to be the month for thru-hikers in Virginia. You don’t mention exactly where you intend to hike, but it is likely that you will encounter thru-hikers throughout Virginia in June. The late starters and/or slowpokes will likely be hitting south and central VA, while the early starters and/or faster hikers will probably be passing through the northern parts of the state and on into MD and PA. It is important to note that, by the time Virginia rolls around, quite a few thru-hikers who started at Springer will have called it quits for various reasons, and those that remain are often traveling with a small group of trail friends rather than with the unwieldy mobs that apparently descend on GA shelters in early spring. As a result, while you will certainly see hikers in June, you are not likely to be overwhelmed and/or crowded out of shelters by them as you might well be in early spring in GA.
I hope this helps.
Ken G.