I ran the following for the weak instrument test:

ivreg2 2sls y (x=z) $covariates i.fixedeffects [aw=perweight], cluster (state)

weakivtest

weakivtest
(obs=200,682)

Montiel-Pflueger robust weak instrument test
--------------------------------------------
Effective F statistic: 0.765
Confidence level alpha: 5%
--------------------------------------------

--------------------------------------------
Critical Values TSLS LIML
--------------------------------------------
% of Worst Case Bias
tau=5% 37.418 37.418
tau=10% 23.109 23.109
tau=20% 15.062 15.062
tau=30% 12.039 12.039
--------------------------------------------

weakiv
(sum of wgt is 2.0218e+11)
Estimating confidence sets over 100 grid points
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100

Weak instrument robust tests and confidence sets for linear IV
H0: beta = 0
------------------------------------------------------------------------------
Test | Statistic p-value | Conf. level Conf. Set
------+---------------------------------+-------------------------------------
AR | chi2(1) = 6.60 0.0102 | 95%
[ ... ,-.421622] U [ .820618, ... ]
------+---------------------------------+-------------------------------------
Wald | chi2(1) = 0.32 0.5687 | 95% [-7.93717, 4.361]
------------------------------------------------------------------------------
Confidence sets estimated for 100 points in [-14.0863, 10.5101].
Number of obs N = 200682.
Method = lagrange multiplier (LM).
Tests robust to heteroskedasticity and clustering on state (N_clust=37).
Wald statistic in last row is based on ivreg2 estimation and is not robust to weak instruments.

Can you help me to understand whether my instrument is weak or not?
When I did weaakivtest, the effective F-stat is very low. How to interpret that? How to interpret AR chi2(1) and the p-value? Also, I get open end confidence interval, which shows the instrument is weak?

I searched in the forums for interpretations, I didn't get much results. any help is appreciated!