you can choose "Average" for "Merged by Y" option in the "Reduce by Group" tool, instead of "Max". The total number of 1's in each bin should be gotten by multiplying the number of cells in a bin, in your case 1000 (=1/0.001). (You need to take care of the last bin if it doesn't fulfill the full bin size.)
thanks, oh well really easy!! Currently writing my diploma thesis and origin is now the last little step of my work and the easiest things seem to be the hardest ones at the moment because of the lack of time