Grippy (high silicone content) and high profile (old school) are mutually exclusive tyre characteristics.
The older Imperial measure tyres will give a higher profile.
e.g. Avon MKII AM7 5.00S16
or Continental K112 5.00H16
These tyre are all weather which is about as grippy as you're going to get
Older style tyres from a high quality company:
Michelin Commander 140/90-16 is the "best fit" metric equivalent, if you can find any. You can go as wide as 150/90-16 which will show more sidewall rubber by virtue of size alone...again, if you can find any.
Hope this helps.
edit: whether or not these widths will fit inside your swingarm is another story.