Does stronger regulation of economic activity impede economic growth in constitutional democracies with basic constitutional rights? Given similar democratic constitutions and basic constitutional rights such as property rights, freedom of speech, freedom of press etc and the definition of regulation according to OECD:

Regulation is broadly defined as imposition of rules by government, backed by the use of penalties that are intended specifically to modify the economic behaviour of individuals and firms in the private sector.

Is there a relationsship between regulation of economic activity and economic growth? Are there any reviews / meta analysis?
Broadly speaking regulation can be defined as done by OECD see Khemani and  Shapiro (1993):

Regulation is broadly defined as imposition of rules by government, backed by the use of penalties that are intended specifically to modify the economic behaviour of individuals and firms in the private sector.

This is broad definition that includes anything from price controls via regulations on export/imports to antitrust laws.
Research shows that inclusive institutions which include things that would very well fall under the label regulation like antitrust laws, laws that enforce competition, prevent firms from creating barriers to entry and so forth do promote economic growth (see Acemoglu 2008, Acemoglu &amp; Robinson 2000a, 2000b, 2001, 2006, 2008; Olson 1984, Bates 1981, 1983, 1989 and sources cited therein*).
On the other hand extractive institutions, such as government grants of monopolies, restrictions on who or what classes of people can participate in labor market (e.g. like many apartheid regulations that restricted blacks form some professions) many of which again would fall under the label of regulation, tend to depress growth (see the same sources as above).
So growth is neither retarded or supported by 'heavy regulation' per se, it all depends what sort of regulation we are talking about. Regulation that fixes market failures, promotes openness and competition generally supports growth whereas regulation that creates market failures, closes economy and favors concentration generally retards growth.
An important caveat is that under a more narrow definitions of regulation such as the definition used by  Breyer et al (2016):

governmental actions to control price, sale and production decisions of firms in an avowed effort to prevent private decision-making

which is more narrow the answer might change as literature is less kind to price controls and command and control regulations, but still the answer would depend on what sort of regulation are we talking about.
In literature,  the focus is not really on how 'heavy' regulation is, but on regulation quality. For example, Jalilian et al (2007) show that developing countries with higher regulatory quality grow faster, where regulatory quality is defined as &quot;burden on business via quantitative regulations, price controls, and other interventions in the economy&quot; (where more burden means lower quality - but burden is not the same as having many regulations as one can implement large quantity of well designed regulations that jointly might have smaller burden than few very badly designed regulations).

* Note this research is also summarised in Acemoglu &amp; Robinson: Why Nations Fail? which is book that is written in a way that is more accessible to laymen readers than the papers mentioned above).