First, this is overly-simplified, because what a "codification of Roe" looks like can be several different things.
RBG had noted that abortion regulations are, primarily, restrictions on medical practice - i.e. what is it that medical professionals, within the range of their expertise, are or are not allowed to do, and that could be a better framing.
For example, let's say that Congress passes a statute that states cannot punish or terminate licenses of physicians who provide abortions under (conditions defined in Planned Parenthood v. Casey) or something to that effect.
In the division between state/federal spheres of power, there are things that are up to states solely, things that are up to Congress solely, and things that overlap. When they overlap, then there are principles for determining whether the federal authority pre-empts state authority.
So, taking that federal law is it:
1. A federal law regulating medical licenses; or
2. A federal law regulating interstate commerce.
Those choices can determine the outcome.
The argument against is that the regulation of the medical profession is a longstanding area of state authority. States issue medical licenses and determine the conditions for getting and keeping them.
The argument for is that restricting the range of reproductive health care options has a substantial impact on interstate commerce.
But, you know what. If five justices want abortion to be illegal in as many states as possible, then they'll find the argument that suits them. That is the bottom line.
For a look at how the "is it interstate commerce" question works, a good reference is US v. Morrison, which struck down part of the Violence Against Women Act as usurping ordinary state police power over assaults and personal injuries:
https://en.wikipedia.org/wiki/United_States_v._Morrison
United States v. Morrison, 529 U.S. 598 (2000), is a U.S. Supreme Court decision that held that parts of the Violence Against Women Act of 1994 were unconstitutional because they exceeded the powers granted to the US Congress under the Commerce Clause and the Fourteenth Amendment's Equal Protection Clause. Along with United States v. Lopez (1995), it was part of a series of Rehnquist Court cases that limited Congress's powers under the Commerce Clause.
The case arose from a challenge to a provision of the Violence Against Women Act that provided victims of gender-motivated violence the right to sue their attackers in federal court. In a majority opinion joined by four other justices, Chief Justice William Rehnquist held that the Commerce Clause gave Congress only the power to regulate activities that were directly economic in nature, even if there were indirect economic consequences. Rehnquist also held that the Equal Protection Clause did not authorize the law because the clause applies only to acts by states, not to acts by private individuals.
Unsurprisingly, it involves the rights of women.
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