Sunny, dry, clay soil flower bed has been taken over by weeds which I pull out but they grow back every year. Can I place rocks and large stones instead of perennials in that sunny, clay soil bed to prevent weeds from growing? Or will weeds grow around the rocks and stones?
The short answer is, sadly, that eventually weeds will emerge around any rocks and large stones that you place in your flower bed, but there are steps you could take to mitigate this. Here is a link to a question we answered a while ago – it is not quite an analogous situation to yours, but there is advice here about how to lay down rocks and stones to minimize weed regrowth: https://www.torontomastergardeners.ca/askagardener/overgrown-weed-patch-river-rock-bed-cathy/
Weeds are pretty amazing in that they have one goal: to reproduce as quickly and efficiently as possible. Many weed species do this by quick flowering and seed production; some single plants produce thousands of seeds that can remain viable in the soil for decades. Others use both seed production and reproduction via underground rhizomatic root systems. Identifying the weed species you have in your flower bed will help in understanding their life cycle, and from there, management strategies. Tackling weeds as they emerge is the best approach in a rock bed.
If you would prefer to have plant material in this flower bed, and would consider another approach, many garden professionals have a strong preference for mulch both for weed suppression and moisture conservation. Here is Canadian garden pro Mark Cullen on the subject: http://www.markcullen.com/low-maintenance-gardening-mulch-mulch-mulch/
There are many perennials that do well in clay soil, both native and non-native, which once established will help to out-compete the weed population. Here is a brief list to peruse: https://landscapeontario.com/these-native-plants-love-clay