I have been requested to put fresh fruit--raspberries and blackberries, as a filling in a cake. I am worried it will make the cake soggy.

Well it depends how you do it. If you just use the fresh berries as they are, then yes they will "weep" after a while. What exactly are you making, a shortcake of some kind? You can make it fresh, with a whipped cream filling and use it immediately and it will be fine.

You can make a cooked filling with the berries if you need it to hold up for more than a day.