Most licenses available do not seem to carry any legal weight. Are there any Open Source licenses that do? The old copyright laws used to impose a monetary fine for infringement, but then how do the newer licenses deal with infringement? What resources do I have available if the terms of the "newer" licenses are broken?
You claim most licenses don't carry any legal weight. But I'm not so sure about this being true. Naturally it is hard to say, how good licenses can be enforced in court, until it happens...
And it happened already and courts enforced open source licenses.
The popularity and flexibility of Linux lead to the wide usage of the kernel in multiple devices, namely routers. Some of the constructors of these routers used the software in violation of the GPL. Harald Welte - developer of the netfilter/iptables - was starting to take legal action against it. His law-suits lead to acknowledgment of the GPL in court. To better defend his claims he founded an organisation named gpl-violations. Some notable wins included cases against Fortinet, D-Link and Skype because of the violation of the GPL. In these cases Welte and gpl-violations won.
gpl-violations also sided with Cybits AG in a law suit against router-producer AVM. Cybits modified the AVM firmware for some goals, and AVM was taking court-action against that. As AVM also used a Linux kernel, FSF and gpl-violations were siding Cybits AG in this case. Also in this case the GPL was acknowledged from the court: https://fsfe.org/activities/ftf/avm-gpl-violation.html
Software Freedom Law Center
Similar to the german based GPL-violations the Software Freedom Law Center enforces the GPL in the US. Notable cases here involve the BusyBox-developers against multiple developers of electronic devices that violated the terms of the license and the FSF against Cisco.
Open Source licenses are enforcable in court. This as always depends on the details of the case and the jurisdiction you're in, but generally the terms of open source licenses can be accepted by courts. It is possible though, that some terms are unclear or not really working in law, because of the missing knowledge of the authors about law. It is for this reason you should prefer common popular licenses (more tested in court) and licenses that are written with the consultations of lawyers.
The GPL seems the license you can be most sure it is enforcable, as that already happened multiple times with differing details in the case and in differing jurisdictions.
It is generally recommendable you look for legal help if you want to enforce the license to your work. gpl-violations as of now seems no longer in action, but in the US you can search the help of the Software Freedom Law Center, also organizations like FSF (and the european version FSFE) might be helpful in case you want to defend your rights given to you from open source software.