Is there a way to distinguish which variable describe the best the parameter of interest when the R² are very close to each others? I try to see if between the weight, the BMI and body surface area, which one des cribes the best my data. The R² for these 3 variables are very close to each others. 
Is there another way to try to see if one is better than the others?
 A: The best test for this specific question would be a "Relative Weights Analysis". Essentially what it does is it takes your three predictors, and creates orthogonally transformed versions of each. Then it estimates the variance explained by each of them by relating the untransformed predictors to the transformed predictors and combines that path with the path of the transformed predictors to the criterion. This returns the proportion of the variance explained that is predicted by each predictor. It also does really well with multicollinearity, which you are almost definitely going to have.
Here's a link that should explain the nitty gritty details of how to run it. There is also a really good package in R called flipRegression that will run it for you and displays the output really nicely. Good luck!
https://link.springer.com/article/10.1007/s10869-014-9351-z
A: I would try PCA analysis. Get the first principal component of all three variables, and use it in regression. It's becoming popular in econometrics these days. You know that all three variables are important, so instead of picking on of three, you pick a linear combination of all three. 
For example, see the last paragraph in section 2.3 of this paper: Mihov, Atanas and Curti, Filippo and Abdymomunov, Azamat, U.S. Banking Sector Operational Losses and the Macroeconomic Environment (July 5, 2017). Available at SSRN: https://ssrn.com/abstract=2738485 or http://dx.doi.org/10.2139/ssrn.2738485 :

To condense the information contained in GDP Growth, HPI Growth, CREPI
  Growth, VIX and BBB-T10 Cred Sprd into a single measure of
  macroeconomic activity, we apply the method of principal component
  analysis (PCA). Following prior studies (e.g., Stock and Watson
  (1999), Ludvigson and Ng (2007), Koopman et al. (2011), Sarlin
  (2016)), we use PCA as a dimension-reduction methodology to relate
  observed variables to a small set of orthogonalized
  factors/components. In our analysis, we focus solely on the first
  principal component as our measure of the macroeconomic environment,
  ME, as it adequately summarizes variation in the underlying data by
  explaining a high proportion of the variables’ variances — 69%.15

You can call you new variable "person size" factor.
