Just looking through my log of my walking activities at the same time last year, I did 9 walks in the last 2 weeks of March and first week in April, and as far as rainfall was concerned, I recorded one drizzle and one heavy snow showers with a general moderate snow cover. The rest was cold, cool, sunny and windy.
So it'll probably chuck it down!
I think its impossible to say, its that time of year when it could persist persistently, or it could be cold and sunny if you're lucky with some high pressure. My own preference would be to go for the heavier jacket, as its still winter up Cross Fell and the Cheviots