Metformin Hydrochloride is used to treat type II diabetes.  It’s possible that Metformin could increase height via a SIRT1 cellular senescence related mechanism, a mitochondrial related mechanism(chondrocytes are hypoxic so metformin could affect height in that way), or another mechanism.

Evaluating the Effects of Metformin Use on Height in Children and Adolescents: A Meta-analysis of Randomized Clinical Trials.

Full study->poi150054

“Metformin hydrochloride use is increasing in children and adolescents. [There’s] a large variability in the effects of metformin use on body mass index changes but have not considered height changes as a confounder{Height affects BMI, Metforim may affect height}.
To conduct a systematic review and meta-analysis of the effects of metformin use on height in children and adolescents.
Computerized databases, including MEDLINE and EMBASE, were searched up to September 9, 2014, for terms related to metformin and childhood or adolescence.
Randomized clinical trials examining the effects of metformin use on height of participants younger than 19 years were considered eligible. Trials with cointerventions other than lifestyle changes were excluded.
Height, weight, body mass index, age, sex, metformin dosage, and study duration were independently extracted by 2 reviewers. The weighted mean differences for changes in height, weight, and body mass index were compared between the metformin and control groups using random-effects models.
Ten studies were included, with a total of 562 participants, 330 (58.7%) of whom were female. The mean age within the studies ranged from 7.9 to 16.1 years, with a high variability in most studies. The duration of metformin interventions lasted from 3 to 48 months. Overall, height changes were not significantly different between the metformin and control groups. However, stratified analyses according to the cumulative metformin dose (in milligrams per day times the number of days of treatment) showed a greater increase in height with metformin use in the 5 studies providing the largest cumulative metformin doses (weighted mean difference, 1.0; 95% CI, 0.0 to 2.0 cm) but not in the 5 studies providing the lowest doses (weighted mean difference, -0.1; 95% CI, -0.7 to 1.0 cm) compared with the control group.
Preliminary evidence suggests a dose-response relationship between metformin use and increases in height in children and adolescents compared with a control group. While an approximate 1-cm increase in height may appear small, it is likely underestimated given that many studies were of short duration and included older adolescents, potentially after epiphyseal growth plate closure.”

Metforrim may have had an impact on height by up to 2cm in subjects that high doses of metforrim.

“A greater cumulative exposure to metformin may increase height by a mean of approximately 1 cm in children and adolescents compared with a control group.”<-A dedicated study is needed though.

“a 2.8-cm greater increase in height in the metformin group for girls approximately 9 years old”

“metformin administration during puberty could enhance or prolong the normally occurring, puberty induced height change”

Does Metformin Really Increase Height, or Is There Some Problem With the Controls?—Reply

“thank Poulton for the thoughtful letter that stated that the greater increase in height observed in studies from our meta-analysis with the highest cumulative metformin dose was owing to “a combination of inaccurate and abnormally slow growth rates in the control individuals.”

We agree that artifacts could arise from a higher attrition level in the study by Kendall et al, and understand why it is tempting for Dr Poulton to suggest that we should reanalyze without this study. However, we disagree that we should exclude an individual study owing to its attrition level without applying this criterion to all studies (eg, the study by Mauras et al had the highest control group attrition rate but a −0.2-cm change in height in the metformin vs the control group). While the changes in height in the control group from Kendall et al (ie, 1 cm in 6 months; mean baseline age of 13.6 years) may seem “suspiciously slow,” it is not dissimilar from other studies we reviewed that were comparable in terms of duration and participants’ baseline age. This “slower growth than normal in the controls” may therefore be explained by findings that suggest children with obesity have an earlier peak height velocity and onset of puberty, but lower peak height velocity. For these reasons, we believe it would be inappropriate for us to single out and exclude the data from Kendall et al.^“

Early metformin therapy to delay menarche and augment height in girls with precocious pubarche

“At age 8 years, girls were randomly assigned to remain untreated or to receive metformin for 4 years; subsequently, both subgroups were followed without treatment until each girl was postmenarcheal.