Your network might be crowded during peak hours, not allowing you the pristine connection most Blizzard games require.
Explanation of why this is a thing is in the stickies: Common Technical Issues and Solutions - #19 by Drakuloth
Post a WinMTR https://us.battle.net/support/en/article/27780 that you run for 5-10 mins during the times you have the most issues. You’ll be pinging the Overwatch servers, and you don’t need to actually play Overwatch while you do it. You can also run it in the background while you do other stuff.