r - Puzzling average of correlated measurements

Question

I submitted this question to stat.stackexchange

https://stats.stackexchange.com/questions/147909/puzzling-average-of-correlated-measurements

but it looks like it fits more into that forum, as it may be more a computing issue than a statistic one:

I want to average correlated measurements. Given a set of measurements:

x = ( x1, x2, x3 )

whose internal correlations are given by the covariance matrix C.

A Chi2 minimization leads to the following average:

<x> = C^-1 * x / C^-1

But the following example puzzled me:

Let's consider the following tree:

tree.mod:

 (((oryLat2:0.3,(HLnotFur1:0.3001,HLxipMac2:0.3001)HLnotFur1-HLxipMac2:0.0001)oryLat2-HLnotFur1:0.05,(gasAcu1:0.01,tetNig2:0.02)gasAcu1-tetNig2:0.1)oryLat2-gasAcu1:0.4,danRer7:0.5)oryLat2-danRer7;

and do in R:

R
library(ape)
# Read the tree
tree <- read.tree( "tree.mod" )

# Extract a clade of 3 species
clade <- extract.clade( phy=tree, node="oryLat2-HLnotFur1")

# Measurements
x <- c(1,4,4)

# Covariance of the clade
V = vcv(clade)
      oryLat2 HLnotFur1 HLxipMac2
oryLat2       0.3    0.0000    0.0000
HLnotFur1     0.0    0.3002    0.0001
HLxipMac2     0.0    0.0001    0.3002

# Replace zero-entries
V[V==0] = 1e-5
      oryLat2 HLnotFur1 HLxipMac2
oryLat2     3e-01   0.00001   0.00001
HLnotFur1   1e-05   0.30020   0.00010
HLxipMac2   1e-05   0.00010   0.30020

# Formulas

# Weights
r <- 1/V
           oryLat2    HLnotFur1    HLxipMac2
oryLat2       3.3        100000   100000
HLnotFur1     100000     3.3      10000
HLxipMac2     100000     10000     3.3

#Mean
meanX = sum(x %*% r) / sum(r)
2.500008

I am puzzled because meanX = 2.5, which corresponds to the case of high correlation, while in that example the covariance matrix is almost diagonal, so I expect meanX = 3.

I must be missing something, any input would be welcome! Thanks