You'll have to better define what you mean by physical/mental addiction.
Tolerance will indeed build up with weekly use, not as fast as constant use but you will find yourself needing more to achieve the same effects. Acute withdrawal (feeling sick on Sunday/Monday after dosing the weekend before) will not be as likely to occur but if it does you'll notice it fairly quickly and, hopefully, be able to reduce your dosage accordingly. PAWS (post acute withdrawal symptoms) may build up without you noticing them. Where if you suddenly stop using on weekends you'll feel listless and irritable as if life isn't as enjoyable as it was before. This relates to "working for the weekend" below as well.
Addiction (whether mental or physical) is generally characterized by not being able to stop and it hurting your life, but different groups have different definitions. I'd suggest you read this thread to see what it is all about chemically in the brain.
http://www.bluelight.ru/vb/threads/566235-The-Basic-Biology-of-Drug-Addiction
"Working for the weekend" is diagnosed by some as a type of drug addiction. You can't stop thinking of just getting through the week to use drugs and not using over the weekend makes life boring and uninteresting etc. It really depends on what your point of view is centered around. Are drugs complimenting or supplementing. As I mentioned this, even casual use, can rewire your brain to expect the drugs on weekends and result in dysphoria if they are presented. Whether you classify them as PAWS (usually reserved for after a major addiction) or just not enjoying things quite as much when not on drugs, is irrelevant.
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What it all comes down to is opioids are chemicals which affect your brain and CNS. Trying to split that up into "mental" and "physical" effects is pretty hopeless and it is better to just consider the brain and body as a whole.