Should I make equally sized samples for the Mann-Whitney U test if originally I have unequal sample sizes I have 2 groups  with unequal sizes (control 70% and test 30%) and need to find out if there is a significant difference between these groups. I've read that MW test works fine with unequal sized samples, but the statistical power  will diminish as the group sizes become more unequal. Hence I was adviced to make groupes of equal sizes  (by multiplying by coefficient). I worry that in this case the stat power will diminish as well, however couldn't find  published references to prove that.
Could anyone help me with advice what I should do : leave it as it is or try making the groups equally sized.
Appreciate all the help)

Use your original data.
Claims about losing power when groups have unequal sizes make more sense in the context of designing the experiment. If you have enough resources to make $100$ observations, the greatest power will be when you allocate $50$ to the control group and the other $50$ to the treatment group. However, $150$ in the control group with $50$ in the treatment group will be more powerful than the test with $100$ observations, even if it is not the most powerful allocation of the $200$ observations.
(It can be defended to do uneven allocation, however. Maybe the treatment is expensive, but you still get adequate power with $50$ treatment subjects and $150$ control subjects.)
