How should I respond to full text requests from other researchers I don't know? I am an early/mid-career academic in a science field and have enough publications where I sometimes get random other academics asking me for electronic copies of papers (published in non-open-access journals) where I am the corresponding author. These papers were done under the purview of NIH grants, which means full text becomes available after a one year embargo.

In the case where the request comes less than one year after publication, how should I respond to such requests? My impulse is just to send the paper without hesitation, but I am unsure if this is "bad form" with regard to the journal. I am seeking the advice of more experienced academics. 

Thanks for any advice.
Journals have "author rights" policies on what you can do with your paper. (e.g.: https://www.elsevier.com/about/our-business/policies/copyright#Author-rights) 
Most I have seen allow exactly this sort of sharing - at least of the pre-publication draft, if not the final formatted version. 

You should look them up for the journal in question. Even if the policy doesn't allow it, send it anyway. Nuts to journals who try to prohibit one of the fundamental aspects of science. 

(The reason to look it up is to never ever again submit to a journal who has this policy.)