When I add 11.23 bank interest from my 1099-int my refund goes from$1031 to $1019. Wy is my refund being reduced by twelve dollors when adding $11.23

The tax tables work in $50 ranges (when the total of all taxable income is over $3000)

Any change within that $50 range doesn't change the taxes assessed....while a jump to the next range will increase yoru tax

so 

a) if your current taxable income is at the bottom of a $50 range, an added (say) $48 may do nothing...while

b) if you are near the next $50 break point, then an added $1 or $2 may push you into the next tax block...jumping your tax $12 (depends exactly where you are in the tables).

Essentially you actually saw $12 tax for a ~$50 change  (~24% since some of the $50 was already waiting in there)