Yes to weight being an issue. I had a canvas bag first time around and quickly ditched it as it was too heavy once I had filled it (especially once you're carrying water bottles, snacks, etc for toddlers).
For me I didn't worry about something my partner would use - he'd only use a 'sporty' rucksack, so I just let him sort himself out.
I like Storsak and had the Olivia bag. Really light, lots of pockets, doesn't scream 'changing bag'. I've even put it in the washing machine a couple of times. A long strap so you can wear it as a sling bag and be hands free, or hang over pram handles are an absolute must for me.