Shop for a gtx 750 ti.
I see them for about a 100 bucks.
It's a small bump up in watts but a big bump up in perf.
As to Overwatch on high I have no idea.
If your going to get serious about gaming do consider an upgrade to that psu.
I have a Acer Aspire M3970 and want to upgrade from my AMD Radeon HD 6570, my budget would be $150 at most, not looking for the best possible graphics card, just one good enough to run a game like Overwatch on high.
Processor: Intel Core i5-2310
CPU: 2.90 GHz
RAM: 6.00 GB