The maximum tire width depends on the frame/fork. What road bike do you have?
Also it's possible that you don't feel stable because the bike doesn't fit you right. Did someone at the bike shop do a fitting when you bought it?
- Gray 2010 carbon WSD road bike, Rivet Independence saddle
- Red hardtail 26" aluminum mountain bike, Bontrager Evoke WSD saddle
- Royal blue 2018 aluminum gravel bike, Rivet Pearl saddle
Gone but not forgotten:
- Silver 2003 aluminum road bike
- Two awesome worn out Juliana saddles