Do you have any symptoms like snoring, interrupted sleep, unrefreshened sleep, morning headaches, daytime sleepiness etc, if yes it further supports the diagnosis.
It is a condition characterised by obstruction of upper airway especially during sleep due to lax airway and narrowing of airway due to obesity.
Basically, obstruction of upper airway leads to temporary stoppage of respiration, increased sympathetic drive and increased pulse rate. Also, other reason for pulse rate rise is deconditioning as you are not accustomed to activities.
ENT examination if you have any symptoms of nasal stuffiness, recurrent tonsillitis to rule nasal causes of obstruction.
Thyroid function test