I'm a little baffled by your question. I've made a simple simulation, data attached:
sum x1 x2 x3 x1_proportion x2_proportion x3_proportion ones
1.44975 .884738 .331214 .233797 .6102698 .2284629 .1612673 1
1.75989 .793748 .655205 .310937 .4510212 .3722992 .1766796 1
1.35571 .462276 .882351 .011085 .3409837 .6508396 .0081768 1
1.63689 .002848 .708656 .925386 .0017398 .4329283 .565332 1
1.44575 .862857 .256457 .326439 .5968218 .1773864 .2257918 1
2.10639 .59055 .964992 .550847 .2803613 .4581261 .2615126 1
1.34527 .180885 .497332 .667048 .1344604 .3696907 .4958489 1
1.97426 .299043 .831939 .843283 .1514706 .4213918 .4271376 1
1.7669 .559657 .268161 .939079 .3167457 .1517697 .5314847 1
1.58345 .916163 .520577 .146706 .5785881 .3287623 .0926496 1
1.77596 .832321 .670544 .273091 .4686608 .3775677 .1537714 1
1.89561 .779795 .756137 .359681 .4113679 .398888 .1897441 1
.784696 .000545 .63612 .148031 .0006939 .810658 .1886481 1
1.63006 .25147 .58731 .791278 .1542705 .3603002 .4854293 1
1.8412 .526846 .327903 .986448 .2861431 .1780925 .5357644 1
1.52932 .627659 .802862 .098797 .4104179 .5249804 .0646017 1
Then in Stata (or whatever you want)
reg sum x1 x2 x3
obtains 1's for all $\beta$'s like anticipated and rounding error to 0 for the constant. $R^2$'s are all 1. But
reg ones x1_proportion x2_proportion x3_proportion, noconst
Obtains, again, all $\beta$s are 1. And if you allow the constant, you will get simply 1 for the constant and 0 for all $\beta$s. In either case, again, $R^2$'s are all 1.
I think you have some confusion about the meaning of regression here, so I will dig deeper and speculate a bit. I think you actually want:
... That x1 represents, on average 32.4% of the "sum" variable, with a standard deviation of 19.6%